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MONKEY.PS
资源名称：diehard.zip　[点击查看]
上传用户：wzoulong
上传日期：2021-03-05
资源大小：732k
文件大小：118k
源码类别：

PropertySheet

开发平台：

Others

MONKEY.PS：源码内容
  1. %!PS-Adobe-2.0
  2. %%Creator: dvipsk 5.58a Copyright 1986, 1994 Radical Eye Software
  3. %%Title: monkey.dvi
  4. %%Pages: 9
  5. %%PageOrder: Ascend
  6. %%BoundingBox: 0 0 596 842
  7. %%DocumentPaperSizes: a4
  8. %%EndComments
  9. %DVIPSCommandLine: dvips monkey
  10. %DVIPSParameters: dpi=300, compressed, comments removed
  11. %DVIPSSource:  TeX output 1996.01.06:0954
  12. %%BeginProcSet: texc.pro
  13. /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N
  14. /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72
  15. mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1}
  16. ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale
  17. isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div
  18. hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul
  19. TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if}
  20. forall round exch round exch]setmatrix}N /@landscape{/isls true N}B
  21. /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B
  22. /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{
  23. /nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N
  24. string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N
  25. end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{
  26. /sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]
  27. N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup
  28. length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{
  29. 128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub
  30. get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data
  31. dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N
  32. /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup
  33. /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx
  34. 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff
  35. setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff
  36. .1 sub]/id ch-image N /rw ch-width 7 add 8 idiv string N /rc 0 N /gp 0 N
  37. /cp 0 N{rc 0 ne{rc 1 sub /rc X rw}{G}ifelse}imagemask restore}B /G{{id
  38. gp get /gp gp 1 add N dup 18 mod S 18 idiv pl S get exec}loop}B /adv{cp
  39. add /cp X}B /chg{rw cp id gp 4 index getinterval putinterval dup gp add
  40. /gp X adv}B /nd{/cp 0 N rw exit}B /lsh{rw cp 2 copy get dup 0 eq{pop 1}{
  41. dup 255 eq{pop 254}{dup dup add 255 and S 1 and or}ifelse}ifelse put 1
  42. adv}B /rsh{rw cp 2 copy get dup 0 eq{pop 128}{dup 255 eq{pop 127}{dup 2
  43. idiv S 128 and or}ifelse}ifelse put 1 adv}B /clr{rw cp 2 index string
  44. putinterval adv}B /set{rw cp fillstr 0 4 index getinterval putinterval
  45. adv}B /fillstr 18 string 0 1 17{2 copy 255 put pop}for N /pl[{adv 1 chg}
  46. {adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{
  47. adv rsh nd}{1 add adv}{/rc X nd}{1 add set}{1 add clr}{adv 2 chg}{adv 2
  48. chg nd}{pop nd}]dup{bind pop}forall N /D{/cc X dup type /stringtype ne{]
  49. }if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup
  50. length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{
  51. cc 1 add D}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin
  52. 0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul
  53. add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore userdict
  54. /eop-hook known{eop-hook}if showpage}N /@start{userdict /start-hook
  55. known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X
  56. /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for
  57. 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0
  58. 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V
  59. {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7
  60. getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false}
  61. ifelse}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale rulex ruley false
  62. RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1
  63. false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave newpath transform
  64. round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg
  65. rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail
  66. {dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}B /c{-4 M}
  67. B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{
  68. 4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{
  69. p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p
  70. a}B /bos{/SS save N}B /eos{SS restore}B end
  71. %%EndProcSet
  72. TeXDict begin 39158280 55380996 1000 300 300 (monkey.dvi)
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  524. %%EndProlog
  525. %%BeginSetup
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  533. %%EndSetup
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  543. (t)o(s)j(as)0 482 y(w)o(ell)g(as)g(t)n(h)o(a)o(t)h(of)f(t)n(h)o(e)h
  544. (pro)o(v)o(erbial)f(monk)o(ey)e(a)o(t)j(a)f(t)o(yp)q(ewr)q(it)o(er.)35
  545. b(Surpr)q(i)q(s)q(in)o(gly)m(,)18 b(m)o(an)o(y)g(que)q(st)o(ions)i(a)o
  546. (b)q(ou)o(t)0 532 y(t)n(h)o(e)15 b(monk)o(ey's)d(lit)o(erary)h(ou)o(t)o
  547. (pu)o(t|t)n(h)o(e)i(t)o(im)o(e)q(s)e(b)q(et)o(w)o(een)i(ap)o(p)q
  548. (earance)q(s)g(of)e(cert)o(ain)i(str)q(in)o(gs,)f(t)n(h)o(e)g(n)n(u)o
  549. (m)n(b)q(er)g(of)0 581 y(di)q(st)o(inct)c(four-let)n(t)o(er)h(w)o(ords)
  550. f(in)f(a)h(milli)o(on)d(k)o(eystrok)o(e)q(s,)12 b(t)n(h)o(e)e(t)o(im)o
  551. (e)f(n)o(ee)q(d)o(e)q(d)j(t)o(o)e(sp)q(ell)f(CA)m(T,)g(for)h
  552. (example|are)0 631 y(w)o(ell)k(suit)o(e)q(d)h(for)g(ass)q(e)q(ss)q(in)o
  553. (g)h(b)q(ot)n(h)f(u)o(niformit)o(y)e(an)o(d)h(in)o(d)o(ep)q(en)o(d)o
  554. (ence)j(in)d(t)n(h)o(e)i(ou)o(t)o(pu)o(t)g(of)e(a)g(ran)o(dom)f(n)n(u)o
  555. (m)n(b)q(er)0 681 y(gen)o(era)o(t)o(or)i((t)n(h)o(e)f(monk)o(ey).)j
  556. (T)m(ec)o(hnically)m(,)11 b(w)o(e)j(are)g(concer)q(n)o(e)q(d)h(wit)n(h)
  557. e(o)o(v)o(erlap)o(pin)o(g)g(m-t)o(uple)q(s)f(of)h(su)o(cce)q(ss)q(iv)o
  558. (e)0 731 y(elem)o(en)o(t)o(s)h(in)f(a)h(ran)o(dom)e(s)q(equence.)62
  559. 781 y(F)m(or)17 b(y)o(ears,)i(in)e(m)o(y)f(ann)n(ual)g(cours)q(e)j
  560. (Compu)o(t)o(er)e(M)o(et)n(h)o(o)q(ds)i(in)e(Proba)o(bilit)o(y)f(an)o
  561. (d)h(St)o(a)o(t)o(i)q(st)o(ics,)g(I)g(calle)q(d)0 830
  562. y(t)n(h)o(e)q(s)q(e)d(Ov)o(erlap)o(pin)o(g)f(m-T)m(uple)d(T)m(e)q(st)o
  563. (s.)19 b(Bu)o(t)14 b(for)f(t)n(h)o(e)g(last)g(few)f(y)o(ears)i(I)f(h)o
  564. (a)o(v)o(e)f(us)q(e)q(d)i(t)n(h)o(e)f(monk)o(ey)f(m)o(et)o(aph)o(or.)0
  565. 880 y(It)i(s)q(eems)g(a)g(b)q(et)n(t)o(er)i(w)o(ay)e(t)o(o)g(st)o(im)n
  566. (ula)o(t)o(e)f(t)n(h)o(e)i(in)o(t)o(ere)q(st)o(s)h(of)e(t)n(h)o(e)h(st)
  567. o(ud)o(en)o(t)o(s)h(an)o(d,)d(b)o(y)h(in)o(v)o(okin)o(g)f(an)h(in)o(t)o
  568. (ere)q(st)o(in)o(g)0 930 y(im)o(age,)d(m)o(ak)o(e)i(t)n(h)o(em)g(more)g
  569. (readily)h(accept)h(t)n(h)o(e)g(id)o(eas)f(an)o(d)g(ev)o(en)g(feel)g
  570. (as)g(t)n(h)o(ough)g(t)n(h)o(ey)h(w)o(ere)g(t)n(h)o(e)q(ir)f(o)o(wn.)62
  571. 980 y(W)m(e)h(h)o(o)o(p)q(e)g(it)g(will)e(h)o(a)o(v)o(e)i(a)g(s)q
  572. (imilar)d(e13ect)17 b(on)e(y)o(ou,)f(t)n(h)o(e)i(read)o(er|not)h(t)n
  573. (h)o(a)o(t)e(I)g(n)o(ece)q(ssar)q(ily)i(equa)o(t)o(e)e(y)o(ou)0
  574. 1030 y(wit)n(h)f(t)n(h)o(e)g(st)o(ud)o(en)o(t)o(s)i((or)e(t)n(h)o(e)h
  575. (monk)o(ey).)62 1080 y(Thi)q(s)f(art)o(icle)f(d)o(e)q(scr)q(ib)q(e)q
  576. (s)i(som)o(e)e(v)o(ery)h(s)q(imple,)d(as)j(w)o(ell)f(as)h(som)o(e)f
  577. (quit)o(e)g(so)o(phi)q(st)o(ica)o(t)o(e)q(d,)g(t)o(e)q(st)o(s)j(t)n(h)o
  578. (a)o(t)e(sh)o(e)q(d)0 1129 y(ligh)o(t)c(on)h(t)n(h)o(e)h(suit)o(a)o
  579. (bilit)o(y)d(of)h(cert)o(ain)i(ran)o(dom)d(n)n(u)o(m)n(b)q(er)i(gen)o
  580. (era)o(t)o(ors.)19 b(Th)o(e)11 b(gen)o(era)o(t)o(ors)i(are)f(us)q(e)q
  581. (d)f(t)o(o)h(pro)o(vid)o(e)0 1179 y(t)n(h)o(e)j(ran)o(dom)e(k)o
  582. (eystrok)o(e)q(s)i(for)f(our)h(monk)o(ey)m(.)i(Th)o(e)e(k)o(eyb)q
  583. (oards)g(ran)o(ge)g(f)q(rom)d(t)n(h)o(e)j(st)o(an)o(d)o(ard)g(26)f(up)o
  584. (p)q(er-cas)q(e)0 1229 y(let)n(t)o(ers)f(t)o(o)f(an)f(organ-lik)o(e)e
  585. (k)o(eyb)q(oard)j(wit)n(h)f(1024)f(k)o(eys)i(t)o(o)f(t)n(h)o(e)h(DNA)g
  586. (k)o(eyb)q(oard)f(wit)n(h)g(four)g(k)o(eys:)17 b(C,G,A,T.)0
  587. 1366 y Fi(2)88 b(CA)-6 b(T)22 b(T)-6 b(e)r(st)o(s)0 1457
  588. y Fl(No)o(w,)16 b(t)o(o)h(bus)q(in)o(e)q(ss.)28 b(St)o(art)17
  589. b(wit)n(h)f(an)g(id)o(ea)i(t)n(h)o(a)o(t)e(pro)o(vid)o(e)q(s)i(a)e(v)o
  590. (ery)h(in)o(e16cien)o(t)f(t)o(e)q(st,)i(bu)o(t)g(on)o(e)e(t)n(h)o(a)o
  591. (t)h(som)o(e)0 1507 y(ran)o(dom)12 b(n)n(u)o(m)n(b)q(er)i(gen)o(era)o
  592. (t)o(ors)i((RNG's))e(f)q(ail.)i(Our)f(monk)o(ey)d((RNG))i(h)o(as)g
  593. (a)g(t)o(yp)q(ewr)q(it)o(er)g(wit)n(h)g(26)g(up)o(p)q(er-)0
  594. 1557 y(cas)q(e)i(let)n(t)o(ers)h(A,B,...,Z)c(t)n(h)o(a)o(t)j(h)o(e)f
  595. (str)q(ik)o(e)q(s)h(a)o(t)f(ran)o(dom.)21 b((Assu)o(m)o(e)16
  596. b(our)f(RNG)f(monk)o(ey)g(pro)q(d)o(u)o(ce)q(s)j(u)o(niform)0
  597. 1607 y(reals)e(in)f([0,1),)f(say)i(b)o(y)f(m)o(eans)g(of)g(a)h(pro)q
  598. (ce)q(d)o(ure)h(UNI().)21 b(Th)o(e)15 b(in)o(t)o(eger)f(part)h(of)f
  599. (26.*UNI())g(pro)o(vid)o(e)q(s)h(t)n(h)o(e)0 1656 y(ran)o(dom)d(k)o
  600. (eystrok)o(e.))20 b(No)o(w)14 b(t)n(h)o(e)h(CA)m(T)f(t)o(e)q(st:)20
  601. b(h)o(o)o(w)14 b(m)o(an)o(y)e(k)o(eys)i(m)n(ust)g(t)n(h)o(e)h(monk)o
  602. (ey)e(str)q(ik)o(e)h(u)o(n)o(t)o(il)g(h)o(e)g(sp)q(ells)0
  603. 1706 y(CA)m(T?)62 1756 y(Th)o(ere)h(are)g(26)293 1741
  604. y Fh(3)323 1756 y Fl(=)d(17)p Fg(;)7 b Fl(576)12 b(p)q(oss)q(ible)j
  605. (3-let)n(t)o(er)g(w)o(ords,)e(so)i(t)n(h)o(e)f(a)o(v)o(erage)h(n)n(u)o
  606. (m)n(b)q(er)e(of)h(k)o(eystrok)o(e)q(s)h(n)o(ece)q(s-)0
  607. 1806 y(sary)e(t)o(o)g(pro)q(d)o(u)o(ce)h(CA)m(T)e(sh)o(ould)g(b)q(e)h
  608. (arou)o(n)o(d)g(17,576,)e(an)o(d)h(t)n(h)o(e)h(t)o(im)o(e)f(t)o(o)h
  609. (reac)o(h)g(CA)m(T)g(sh)o(ould)f(b)q(e)h(v)o(ery)g(clos)q(e)0
  610. 1856 y(t)o(o)g(exp)q(on)o(en)o(t)o(ially)e(di)q(str)q(ibu)o(t)o(e)q(d.)
  611. 18 b(Exact)13 b(an)o(d)g(ap)o(pro)o(xim)o(a)o(t)o(e)d(di)q(str)q(ibu)o
  612. (t)o(ions,)i(an)o(d)g(more)g(e16cien)o(t)h(t)o(e)q(st)o(s,)i(are)0
  613. 1906 y(b)q(ello)o(w;)d(for)i(no)o(w,)f(let's)h(try)g(t)n(hi)q(s)f(s)q
  614. (imple)f(CA)m(T)h(t)o(e)q(st)i(for)f(a)g(few)f(common)f(RNG's.)62
  615. 1955 y(Th)o(e)17 b(con)o(gruen)o(t)o(ial)g(monk)o(ey)m(,)e
  616. Fg(I)20 b Fl(=)d(69069)10 b Ff(03)h Fg(I)k Fl(mo)q(d)c(2)932
  617. 1940 y Fh(32)966 1955 y Fl(,)18 b(con)o(v)o(ert)o(in)o(g)f(t)o(o)g(a)g
  618. (real)g(UNI)g(on)g([0,1),)f(get)o(s)0 2005 y(CA)m(T)d(aft)o(er)h
  619. (13,561)e(k)o(eystrok)o(e)q(s,)j(t)n(h)o(en)g(aft)o(er)f(18,263,)e(t)n
  620. (h)o(en)i(anot)n(h)o(er)h(14,872)d(strok)o(e)q(s)j(pro)q(d)o(u)o(ce)q
  621. (s)g(t)n(h)o(e)g(t)n(hird)0 2055 y(CA)m(T.)e(Quit)o(e)h(sa)o(t)o(i)q
  622. (sf)q(act)o(ory)m(.)62 2105 y(No)o(w)h(cons)q(id)o(er)h(t)n(h)o(e)g
  623. (shift-regi)q(st)o(er)f((T)m(a)n(us)q(ew)o(ort)n(h)o(e))i(monk)o(ey)c
  624. (t)n(h)o(a)o(t)i(pro)q(d)o(u)o(ce)q(s)i(31-bit)d(in)o(t)o(egers)i(b)o
  625. (y)f(ex-)0 2155 y(clus)q(iv)o(e)e(or's,)f(left)h(shift)g(28)g(an)o(d)g
  626. (r)q(igh)o(t)f(shift)h(3.)k(Thi)q(s)c(i)q(s)f(t)n(h)o(e)i(v)o(ery)g
  627. (gen)o(era)o(t)o(or)g(sugge)q(st)o(e)q(d)h([8)o(])e(as)g(a)g(replace-)0
  628. 2204 y(m)o(en)o(t)g(for)h(con)o(gruen)o(t)o(ial)f(gen)o(era)o(t)o(ors)j
  629. (aft)o(er)e(di)q(sco)o(v)o(ery)g(of)g(t)n(h)o(e)q(ir)h(la)o(t)n(t)o
  630. (ice)f(stru)o(ct)o(ure)i([3)o(].)i(Th)o(e)c(shift-regi)q(st)o(er)0
  631. 2254 y(monk)o(ey)f(n)o(ev)o(er)j(sp)q(ells)f(CA)m(T,)f(ev)o(en)h(aft)o
  632. (er)g(t)o(w)o(o)f(million)e(k)o(eystrok)o(e)q(s.)22 b(He)15
  633. b(can't)g(get)g(KA)m(T,)f(DOG,)g(GOD,)0 2304 y(SEX,)d(W)o(O)o(W)g(or)h
  634. (ZIG)f(e)q(it)n(h)o(er.)18 b(Bu)o(t)13 b(h)o(e)f(can)f(get)h(ZA)o(G,)f
  635. (an)o(d)g(t)o(o)q(o)h(oft)o(en|ev)o(ery)g(few)f(t)n(h)o(ousan)o(d)h(k)o
  636. (eystrok)o(e)q(s.)0 2354 y(In)o(d)o(ee)q(d,)j(it)f(t)o(ur)q(ns)h(ou)o
  637. (t)f(t)n(h)o(a)o(t)h(t)n(hi)q(s)f(monk)o(ey)e(w)o(as)j(only)e(a)o(ble)h
  638. (t)o(o)g(get)h(7,834)d(of)i(t)n(h)o(e)h(p)q(oss)q(ible)g(17,576)d
  639. (3-let)n(t)o(er)0 2404 y(w)o(ords,)j((in)g(a)f(str)q(in)o(g)i(of)e
  640. (1,000,000)e(k)o(eystrok)o(e)q(s))17 b(an)o(d)d(of)h(cours)q(e)h(wit)n
  641. (h)f(hi)q(s)f(limit)o(e)q(d)f(v)o(o)q(ca)o(bulary)m(,)h(h)o(e)h(get)o
  642. (s)0 2453 y(t)n(h)o(os)q(e)g(w)o(ords)f(t)o(o)q(o)g(oft)o(en.)62
  643. 2503 y(Not)o(e)g(t)n(h)o(a)o(t)f(in)o(a)o(bilit)o(y)e(t)o(o)j(get)f(CA)
  644. m(T)g(sh)o(ould)g(not)g(b)q(e)g(a)o(t)n(tr)q(ibu)o(t)o(e)q(d)i(t)o(o)e
  645. (t)n(h)o(e)h(equiv)n(alen)o(t)e(of)h(brok)o(en)h(k)o(eys)f(on)0
  646. 2553 y(t)n(h)o(e)g(t)o(yp)q(ewr)q(it)o(er.)18 b(Thi)q(s)12
  647. b(monk)o(ey)g(st)o(ill)f(t)o(yp)q(e)q(s)j(eac)o(h)f(of)f(t)n(h)o(e)i
  648. (let)n(t)o(ers)g(A)f(t)o(o)g(Z)g(wit)n(h)g(t)n(h)o(e)g(exp)q(ect)o(e)q
  649. (d)h(f)q(requencie)q(s)0 2603 y((an)o(d)k(t)n(h)n(us)i(w)o(ould)d
  650. (pass)j(a)e(st)o(an)o(d)o(ard)h(t)o(e)q(st)h(for)e(let)n(t)o(er)i(f)q
  651. (requency).)32 b(F)m(or)18 b(example,)g(26,000)f(k)o(eystrok)o(e)q(s)0
  652. 2653 y(pro)q(d)o(u)o(ce)q(d)d(984)e(C's,)h(967)f(A's)g(an)o(d)h(1021)f
  653. (T's,)g(quit)o(e)h(sa)o(t)o(i)q(sf)q(act)o(ory)m(.)k(Y)m(et)c(con)o(t)o
  654. (in)n(uin)o(g)f(t)n(h)o(e)i(ru)o(n)g(t)o(o)f(2,600,000)0
  655. 2703 y(k)o(eystrok)o(e)q(s)i(f)q(aile)q(d)e(t)o(o)h(pro)q(d)o(u)o(ce)h
  656. (a)e(s)q(in)o(gle)h(CA)m(T!)62 2752 y(As)k(s)q(illy)d(as)j(it)e(s)q
  657. (eems,)i(t)n(hi)q(s)f(i)q(s)g(a)f(v)o(ery)i(e13ect)o(iv)o(e)h(an)o(d)
  658. d(con)o(vincin)o(g)h(w)o(ay)g(t)o(o)g(sh)o(o)o(w)g(t)n(h)o(e)h(u)o
  659. (nsuit)o(a)o(bilit)o(y)0 2802 y(of)g(cert)o(ain)h(ran)o(dom)d(n)n(u)o
  660. (m)n(b)q(er)j(gen)o(era)o(t)o(ors.)33 b(Y)m(ou)18 b(m)o(ay)e(eas)q(ily)
  661. i(wr)q(it)o(e)g(a)g(program)f(an)o(d)h(try)h(it)f(y)o(ours)q(elf.)845
  662. 2978 y(1)p eop
  663. %%Page: 2 2
  664. 2 1 bop 0 45 a Fl(Al)o(t)n(h)o(ough)12 b(d)o(et)o(ails)g(h)o(a)o(v)o(e)
  665. g(b)q(een)h(lost,)f(I)g(rem)o(em)n(b)q(er)f(us)q(in)o(g)g(t)n(h)o(e)i
  666. (CA)m(T)f(t)o(e)q(st)h(t)o(o)f(sh)o(o)q(ot)h(do)o(wn)e(RNG's)h(pro)o
  667. (vid)o(e)q(d)0 95 y(wit)n(h)i(A)n(p)o(ple)f(an)o(d)h(Radio)e(Sh)o(ac)o
  668. (k)i(compu)o(t)o(ers)g((TRS80's)f(?))18 b(wh)o(en)d(t)n(h)o(ey)f
  669. (14rst)h(cam)o(e)e(ou)o(t)h(in)g(t)n(h)o(e)g(1970's.)0
  670. 232 y Fi(3)88 b(More)21 b(E16cien)n(t)h(T)-6 b(e)r(st)o(s)0
  671. 323 y Fl(Most)13 b(of)e(our)g(RNG)g(monk)o(ey's)f(ou)o(t)o(pu)o(t)j(i)q
  672. (s)e(w)o(ast)o(e)q(d)h(if)f(w)o(e)h(only)f(cou)o(n)o(t)h(t)n(h)o(e)h(n)
  673. n(u)o(m)n(b)q(er)e(of)g(k)o(eystrok)o(e)q(s)i(b)q(et)o(w)o(een)0
  674. 373 y(su)o(cce)q(ss)q(iv)o(e)g(ap)o(p)q(earance)q(s)g(of)d(CA)m(T,)h
  675. (DOG)f(or)h(som)o(e)f(su)o(c)o(h)i(3-let)n(t)o(er)g(w)o(ord.)17
  676. b(So,)11 b(inst)o(ead,)h(sup)o(p)q(os)q(e)g(w)o(e)f(cou)o(n)o(t)0
  677. 423 y(t)n(h)o(e)g(f)q(requencie)q(s)h(of)e(all)g(t)n(h)o(e)h(p)q(oss)q
  678. (ible)g(3-let)n(t)o(er)h(w)o(ords)f(pro)q(d)o(u)o(ce)q(d)g(in)f(a)h
  679. (str)q(in)o(g)g(of,)f(say)h(1,757,603)d(k)o(eystrok)o(e)q(s)0
  680. 473 y((t)n(h)o(e)13 b(extra)g(3)f(so)g(t)n(h)o(a)o(t)h(w)o(e)f(h)o(a)o
  681. (v)o(e)g(exact)n(ly)h(1,757,600)c(3-let)n(t)o(er)14 b(w)o(ords,)e(an)o
  682. (d)g(our)g(exp)q(ect)o(e)q(d)i(f)q(requency)f(i)q(s)f(100)0
  683. 522 y(for)j(eac)o(h)i(part)o(icular)e(w)o(ord).)24 b(W)m(e)15
  684. b(n)o(ee)q(d)i(an)e(array)h(of)f(17576)g(elem)o(en)o(t)o(s)h(t)o(o)g
  685. (cou)o(n)o(t)g(t)n(h)o(e)g(f)q(requencie)q(s.)25 b(Let)0
  686. 572 y Fg(x)24 578 y Fh(1)42 572 y Fg(;)7 b(x)85 578 y
  687. Fh(2)103 572 y Fg(;)g(:)g(:)g(:)e(;)i(x)220 578 y Fh(17576)318
  688. 572 y Fl(b)q(e)14 b(t)n(h)o(e)g(obs)q(erv)o(e)q(d)i(cou)o(n)o(t)o(s.)62
  689. 622 y(T)m(ec)o(hnically)m(,)e(t)n(h)o(e)j Fg(x)p Fl('s)e(are)h(asympt)o
  690. (ot)o(ically)d(join)o(t)n(ly)h(norm)o(ally)f(di)q(str)q(ibu)o(t)o(e)q
  691. (d)j((t)n(h)o(ey)h(are)f(m-d)o(ep)q(en)o(d)o(en)o(t)0
  692. 672 y(v)n(ar)q(ia)o(ble)q(s),)k(an)o(d)g(t)n(h)o(e)h(ap)o(pro)o(pr)q
  693. (ia)o(t)o(e)e(st)o(a)o(t)o(i)q(st)o(ical)g(t)o(e)q(st)i(i)q(s)f(t)n(h)o
  694. (e)h(quadra)o(t)o(ic)e(form)g(in)g(t)n(h)o(e)i(w)o(eak)g(in)o(v)o(ers)q
  695. (e)g(of)0 722 y(t)n(h)o(e)g(co)o(v)n(ar)q(iance)f(m)o(a)o(tr)q(ix)f(of)
  696. h(t)n(h)o(e)h Fg(x)p Fl('s,)g(t)n(h)o(a)o(t)g(i)q(s)f(t)n(h)o(e)h
  697. (quadra)o(t)o(ic)f(form)f(in)h(t)n(h)o(e)i(v)n(ar)q(ia)o(ble)q(s)d
  698. Fg(x)1484 728 y Fh(1)1509 722 y Ff(00)7 b Fl(100)p
  699. Fg(;)g(x)1654 728 y Fh(2)1678 722 y Ff(00)0 771 y Fl(100)p
  700. Fg(;)g(:)g(:)g(:)t(;)g(x)179 777 y Fh(17576)268 771 y
  701. Ff(00)e Fl(100)17 b(wit)n(h)g(co)q(e16cien)o(t)o(s)i(t)n(h)o(e)f
  702. (elem)o(en)o(t)o(s)g(of)f(an)o(y)g(w)o(eak)h(in)o(v)o(ers)q(e)g
  703. Fg(C)1354 756 y Fe(00)1399 771 y Fl(of)f(t)n(h)o(e)h(co)o(v)n(ar)q
  704. (iance)0 821 y(m)o(a)o(tr)q(ix)10 b(of)i(t)n(h)o(e)h
  705. Fg(x)p Fl('s.)k((If)c(t)n(h)o(a)o(t)f(co)o(v)n(ar)q(iance)g(m)o(a)o
  706. (tr)q(ix)e(i)q(s)i Fg(C)s Fl(,)g(t)n(h)o(en)h(a)g(w)o(eak)f(in)o(v)o
  707. (ers)q(e)i Fg(C)1294 806 y Fe(00)1334 821 y Fl(sa)o(t)o(i)q(s14e)q
  708. (s)f Fg(C)s(C)1551 806 y Fe(00)1578 821 y Fg(C)h Fl(=)e
  709. Fg(C)s Fl(,)0 871 y(an)o(d)i(t)n(h)o(e)g(v)n(alue)f(of)h(t)n(h)o(e)g
  710. (quadra)o(t)o(ic)g(form)e(i)q(s)h(in)o(v)n(ar)q(ian)o(t)f((wit)n(h)i
  711. (proba)o(bilit)o(y)e(1))i(u)o(n)o(d)o(er)h(c)o(h)o(oice)f(of)g
  712. Fg(C)1559 856 y Fe(00)1586 871 y Fl(.))62 921 y(Not)o(e)c(t)n(h)o(a)
  713. o(t)f(t)n(h)o(e)h(quadra)o(t)o(ic)f(form)e(06(obs)q(erv)o(e)q(d-exp)
  714. q(ect)o(e)r(d)s())969 906 y Fh(2)987 921 y Fg(=)p Fl(exp)q(ect)o(e)q
  715. (d)r(,)i(P)o(earson's)i(class)q(ical)e(c)o(hi-square,)0
  716. 971 y(i)q(s)16 b(not)g(t)n(h)o(e)i(ap)o(pro)o(pr)q(ia)o(t)o(e)d(t)o(e)q
  717. (st.)27 b(Th)o(a)o(t)17 b(t)o(e)q(st)g(ap)o(plie)q(s)f(only)g(for)g(t)n
  718. (h)o(e)h(class)q(ical)f(o)q(ccupancy)i(problem)d((m)n(ul-)0
  719. 1020 y(t)o(inomial)h(di)q(str)q(ibu)o(t)o(ion),)j(wh)o(ere)q(in)g
  720. (balls)f(are)i(pu)o(t)f(in)o(t)o(o)g(cells)g(in)o(d)o(ep)q(en)o(d)o(en)
  721. o(t)n(ly)m(.)33 b(Here)21 b(w)o(e)e(do)f(not)h(h)o(a)o(v)o(e)0
  722. 1070 y(in)o(d)o(ep)q(en)o(d)o(ence;)f(increm)o(en)o(t)o(in)o(g)e(t)n(h)
  723. o(e)g(cou)o(n)o(t)h(for,)e(say)m(,)h(QCA)g(cert)o(ainly)g(in15uence)q
  724. (s)i(a)d(p)q(oss)q(ible)h(increm)o(en)o(t)0 1120 y(for)i
  725. (CAA,CAB,...,CAZ,)e(whic)o(h)o(ev)o(er)j(t)n(h)o(e)g(n)o(ext)g(k)o
  726. (eystrok)o(e)g(br)q(in)o(gs,)g(bu)o(t)g(do)q(e)q(s)g(not)f(in15uence)
  727. i(p)q(oss)q(ible)0 1170 y(increm)o(en)o(t)o(s)14 b(t)o(o)g(t)n(h)o(e)h
  728. (ot)n(h)o(er)g(cells.)62 1220 y(Bu)o(t)j(it)e(t)o(ur)q(ns)h(ou)o(t)f
  729. ((s)q(ee)i([4)o(]))f(t)n(h)o(a)o(t)f(w)o(e)h(get)g(t)n(h)o(e)g
  730. (correct)h((or)f(ra)o(t)n(h)o(er,)g Fj(a)g Fl(correct))h(quadra)o(t)o
  731. (ic)e(form)f(b)o(y)0 1270 y(ap)o(plyin)o(g)e(P)o(earson's)i(form)d(t)o
  732. (wice:)19 b(If)14 b(w)o(e)h(n)o(aiv)o(ely)e(get)h(P)o(earsons)i(quadra)
  733. o(t)o(ic)e(form)e(for)i(t)n(h)o(e)h(3-let)n(t)o(er)g(w)o(ord)0
  734. 1319 y(cou)o(n)o(t)o(s)g Fg(u)153 1325 y Fh(1)172 1319
  735. y Fg(;)7 b(u)215 1325 y Fh(2)233 1319 y Fg(;)g(:)g(:)g(:)t(;)g(u)349
  736. 1325 y Fh(17576)433 1319 y Fl(:)627 1407 y Fg(Q)660 1413
  737. y Fh(3)690 1407 y Fl(=)733 1355 y Fd(i)p Fh(=17576)763
  738. 1367 y Fc(X)767 1456 y Fd(i)p Fh(=1)865 1379 y Fl(()p
  739. Fg(u)905 1385 y Fd(i)928 1379 y Ff(00)j Fl(100))1049
  740. 1364 y Fh(2)p 865 1397 202 2 v 935 1435 a Fl(100)1072
  741. 1407 y Fg(;)0 1518 y Fl(an)o(d)15 b(if)f(w)o(e)h(also)f(cou)o(n)o(t)i
  742. (t)n(h)o(e)g(f)q(requencie)q(s)g(of)f(2-let)n(t)o(er)g(w)o(ords)h(in)e
  743. (t)n(h)o(e)i(14rst)g(1,757,602)c(k)o(eystrok)o(e)q(s)17
  744. b(an)o(d)d(us)q(e)0 1568 y(t)n(h)o(e)h(n)o(aiv)o(e)e(P)o(earson)i(form)
  745. d(for)i(2-let)n(t)o(er)h(w)o(ords)f(wit)n(h)g(exp)q(ect)o(e)q(d)h(cell)
  746. f(cou)o(n)o(t)o(s)h(2600:)635 1697 y Fg(Q)668 1703 y
  747. Fh(2)698 1697 y Fl(=)741 1645 y Fd(i)p Fh(=676)755 1657
  748. y Fc(X)758 1746 y Fd(i)p Fh(=1)840 1669 y Fl(()p Fg(v)876
  749. 1675 y Fd(i)900 1669 y Ff(00)9 b Fl(2600))1041 1654
  750. y Fh(2)p 840 1687 219 2 v 908 1725 a Fl(2600)1064 1697
  751. y Fg(;)0 1824 y Fl(wh)o(ere)k Fg(v)137 1830 y Fh(1)156
  752. 1824 y Fg(;)7 b(v)195 1830 y Fh(2)213 1824 y Fg(;)g(:)g(:)g(:)e(;)i(v)
  753. 326 1830 y Fh(676)389 1824 y Fl(are)12 b(t)n(h)o(e)g(cou)o(n)o(t)o(s)h
  754. (for)f(t)n(h)o(e)g(p)q(oss)q(ible)g(2-let)n(t)o(er)h(w)o(ords,)f(t)n(h)
  755. o(en)g(t)n(h)o(e)h(di13erence,)g Fg(Q)1586 1830 y Fh(3)1610
  756. 1824 y Ff(00)5 b Fg(Q)1680 1830 y Fh(2)1698 1824 y
  757. Fl(,)0 1874 y(i)q(s)19 b(a)h(zero-cen)o(t)o(ere)q(d)j(quadra)o(t)o(ic)c
  758. (form)f(in)i(a)g(w)o(eak)g(in)o(v)o(ers)q(e)g(of)g(t)n(h)o(e)g(co)o(v)n
  759. (ar)q(iance)g(m)o(a)o(tr)q(ix)e(of)h(t)n(h)o(e)i(cou)o(n)o(t)o(s)0
  760. 1924 y Fg(x)24 1930 y Fh(1)42 1924 y Fg(;)7 b(:)g(:)g(:)e(;)i(x)159
  761. 1930 y Fh(17576)243 1924 y Fl(,)18 b(an)o(d)f(i)q(s)f(t)n(h)o(e)i(ap)o
  762. (pro)o(pr)q(ia)o(t)o(e)f((lik)o(elih)o(o)q(o)q(d)e(ra)o(t)o(io))i(t)o
  763. (e)q(st)h(t)n(h)o(a)o(t)g(t)n(h)o(e)g Fg(x)p Fl('s)f(cam)o(e)f(f)q(rom)
  764. f(a)i(norm)o(al)0 1974 y(di)q(str)q(ibu)o(t)o(ion)c(wit)n(h)h(t)n(h)o
  765. (e)g(sp)q(eci14e)q(d)h(m)o(eans)f(an)o(d)f(co)o(v)n(ar)q(iance)h(m)o
  766. (a)o(tr)q(ix.)62 2024 y(If)e(t)n(h)o(e)h(h)o(yp)q(ot)n(h)o(e)q(s)q(i)q
  767. (s)f(i)q(s)g(true)h((t)n(h)o(e)g(monk)o(ey)e(i)q(s)g(str)q(ikin)o(g)h
  768. (t)n(h)o(e)h(k)o(eys)g(u)o(niformly)d Fk(and)k(indep)n(endently)p
  769. Fl(),)f(t)n(h)o(en)0 2073 y Fg(Q)33 2079 y Fh(3)59 2073
  770. y Ff(00)8 b Fg(Q)132 2079 y Fh(2)163 2073 y Fl(will)k(h)o(a)o(v)o(e)h
  771. (a)f(c)o(hi-square)i(di)q(str)q(ibu)o(t)o(ion)e(wit)n(h)h(26)923
  772. 2058 y Fh(3)949 2073 y Ff(00)8 b Fl(26)1031 2058 y
  773. Fh(2)1062 2073 y Fl(d)o(egree)q(s)15 b(of)e(f)q(ree)q(dom,)e((t)n(h)o
  774. (e)j(rank)f(of)g Fg(C)s Fl().)0 2211 y Fi(4)99 b(Spars)q(e)32
  775. b(Occupancy)h(T)-6 b(e)r(st)o(s:)51 b(OPSO,)32 b(OTSO,)g(OQSO)f(an)n(d)
  776. 99 2285 y(DNA)0 2376 y Fl(Wh)o(a)o(t)13 b(if)g(w)o(e)g(w)o(an)o(t)g(t)o
  777. (o)h(ap)o(ply)e(t)n(h)o(e)j(a)o(b)q(o)o(v)o(e)e(t)o(e)q(st)i(t)o(o,)e
  778. (say)m(,)g(4-let)n(t)o(er)h(w)o(ords?)k(W)m(e)13 b(migh)o(t)f(t)o(ak)o
  779. (e)h(a)h(str)q(in)o(g)f(of)g(t)o(w)o(o)0 2426 y(millio)o(n)e(k)o
  780. (eystrok)o(e)q(s)k(an)o(d)f(cou)o(n)o(t)g(t)n(h)o(e)h(f)q(requencie)q
  781. (s)g(of)e(all)f(t)n(h)o(e)j(p)q(oss)q(ible)f(26)1187
  782. 2411 y Fh(4)1217 2426 y Fl(=)d(456976)i(four-let)n(t)o(er)h(w)o(ords.)0
  783. 2476 y(Bu)o(t)k(t)n(h)o(a)o(t)g(require)q(s)g(an)g(array)f(of)f
  784. (456,976)g(elem)o(en)o(t)o(s.)28 b(Th)o(a)o(t)17 b(m)o(an)o(y)f(b)o(yt)
  785. o(e)q(s)i(will)d(do,)j(if)e(t)n(h)o(e)i(f)q(requencie)q(s)0
  786. 2526 y(are)g(100)f(or)h(so.)29 b(Th)o(a)o(t's)17 b(h)o(alf)g(a)g(m)o
  787. (eg)g(of)g(b)o(yt)o(e)q(s|quit)o(e)h(a)f(few.)29 b(W)m(e)18
  788. b(migh)o(t)d(m)o(an)o(age)h(wit)n(h)i(a)f(carefully)0
  789. 2576 y(t)o(ailore)q(d)c(program,)f(bu)o(t)j(w)o(e)f(are)h(pre)q(ss)q
  790. (in)o(g)g(t)n(h)o(e)g(limit.)g(Cou)o(n)o(t)o(in)o(g)f(5-t)o(uple)f(or)h
  791. (6-t)o(uple)f(f)q(requencie)q(s)j(s)q(eems)0 2625 y(b)q(ey)o(on)o(d)g
  792. (reac)o(h.)25 b((Not)o(e)17 b(t)n(h)o(a)o(t,)f(in)g(ord)o(er)h(t)o(o)f
  793. (in)o(v)o(ok)o(e)f(asympt)o(ot)o(ic)g(join)o(t)g(norm)o(alit)o(y)f(for)
  794. h(t)n(h)o(e)i(m-d)o(ep)q(en)o(d)o(en)o(t)0 2675 y(cell)12
  795. b(cou)o(n)o(t)o(s,)i(w)o(e)f(n)o(ee)q(d)g(exp)q(ect)o(e)q(d)h(cou)o(n)o
  796. (t)o(s)g(of)d(som)o(e)h(20)g(or)g(more,)f(so)i(w)o(e)f(will)f(n)o(ee)q
  797. (d)j(a)o(t)e(least)h(6)f(bit)o(s)h(for)f(eac)o(h)0 2725
  798. y(cell.))62 2775 y(An)o(d)h(y)o(et)g(4-,5-,6-t)o(uple)q(s,)d(an)o(d)j
  799. (lon)o(ger,)g(are)g(wh)o(ere)h(w)o(e)e(are)i(more)d(lik)o(ely)h(t)o(o)h
  800. (14n)o(d)f(u)o(n)o(accept)o(a)o(ble)i(ou)o(t)o(pu)o(t)0
  801. 2825 y(f)q(rom)e(our)i(RNG)f(monk)o(eys.)845 2978 y(2)p
  802. eop
  803. %%Page: 3 3
  804. 3 2 bop 62 45 a Fl(Wh)o(a)o(t)14 b(t)o(o)g(do?)19 b(My)14
  805. b(ap)o(proac)o(h)g(i)q(s)f(t)n(hi)q(s:)19 b(inst)o(ead)14
  806. b(of)g(cou)o(n)o(t)o(in)o(g)g(f)q(requencie)q(s)i(of,)d(say)m(,)g
  807. (4-let)n(t)o(er)i(w)o(ords)f(in)0 95 y(a)g(lon)o(g)f(str)q(in)o(g)h(of)
  808. g(k)o(eystrok)o(e)q(s,)h(requir)q(in)o(g)f(a)f(m)o(emory)f(lo)q(ca)o(t)
  809. o(ion|or)g(a)o(t)i(least)h(a)e(b)o(yt)o(e|for)h(eac)o(h)h(p)q(oss)q
  810. (ible)0 145 y(4-let)n(t)o(er)f(w)o(ord,)e(wh)o(y)h(not)g(just)g(cou)o
  811. (n)o(t)g(t)n(h)o(e)h(pre)q(s)q(ence)h(or)e(a)o(bs)q(ence)h(of)e(eac)o
  812. (h)i(p)q(oss)q(ible)f(w)o(ord?)18 b(Th)o(a)o(t)13 b(require)q(s)0
  813. 195 y(a)g(s)q(in)o(gle)g(bit)g(for)g(eac)o(h)i(p)q(oss)q(ible)e(w)o
  814. (ord,)g(or)h(26)733 179 y Fh(4)762 195 y Fl(=)e(456796)g(bit)o(s)i(for)
  815. f(4-let)n(t)o(er)h(w)o(ords)g(in)f(an)g(alph)o(a)o(b)q(et)g(of)f(26)0
  816. 244 y(let)n(t)o(ers.)26 b(Th)o(a)o(t's)16 b(a)o(b)q(ou)o(t)g(14,000)f
  817. (compu)o(t)o(er)h((32-bit))f(w)o(ords,)h(a)g(reason)o(a)o(bly-s)q
  818. (ize)q(d)g(array)g(for)g(most)g(high)0 294 y(lev)o(el)e(lan)o(guage)q
  819. (s.)62 344 y(I)g(call)f(t)n(h)o(e)q(s)q(e)j Fk(sp)n(arse-o)n(c)n(cup)n
  820. (ancy)e Fl(t)o(e)q(st)o(s.)20 b(Beca)n(us)q(e)d(cou)o(n)o(t)o(in)o(g)d
  821. (act)o(ual)f(f)q(requencie)q(s)i(require)q(s)h(arrays)e(t)o(o)q(o)0
  822. 394 y(large,)h(w)o(e)h(only)e(cou)o(n)o(t)i(t)n(h)o(e)g(n)n(u)o(m)n(b)q
  823. (er)f(of)g(empt)o(y)f(cells,)i(t)n(h)o(a)o(t)f(i)q(s,)g(in)g(a)g(lon)o
  824. (g)g(str)q(in)o(g)g(of)g(k)o(eystrok)o(e)q(s,)i(w)o(e)e(us)q(e)0
  825. 444 y(a)i(bit)g(m)o(ap)f(t)o(o)i(14n)o(d)f(h)o(o)o(w)g(m)o(an)o(y)f
  826. (4-)h((5-,6-)f(or)h(high)o(er-))h(let)n(t)o(er)h(w)o(ords)e(are)h(mi)
  827. q(ss)q(in)o(g.)27 b(Som)o(e)16 b(in)o(t)o(ere)q(st)o(in)o(g)0
  828. 493 y(proba)o(bilit)o(y)c(t)n(h)o(eory)j(i)q(s)e(require)q(d)i(t)o(o)f
  829. (d)o(ev)o(elo)o(p)g(ap)o(pro)o(pr)q(ia)o(t)o(e)f(t)o(e)q(st)o(s.)0
  830. 631 y Fi(5)88 b(Th)n(e)22 b(OPSO)f(T)-6 b(e)r(st)0 722
  831. y Fl(Here)17 b(OPSO)f(m)o(eans)e(Ov)o(erlap)o(pin)o(g-P)o(airs-Spars)q
  832. (e-Occupancy)m(.)24 b(W)m(e)15 b(obs)q(erv)o(e)h(2-let)n(t)o(er)g(w)o
  833. (ords)g(in)f(a)f(lon)o(g)0 771 y(s)q(equence)i(of)e(k)o(eystrok)o(e)q
  834. (s)h(f)q(rom)d(an)i(alph)o(a)o(b)q(et)g(of)f(2)817 756
  835. y Fh(10)866 771 y Fl(let)n(t)o(ers.)21 b(By)15 b(s)q(et)n(t)o(in)o(g)g
  836. (a)f(bit,)f(w)o(e)h(m)o(ar)o(k)g(t)n(h)o(e)g(pre)q(s)q(ence)0
  837. 821 y(or)i(a)o(bs)q(ence)i(of)e(ev)o(ery)h(p)q(oss)q(ible)g(2-let)n(t)o
  838. (er)g(w)o(ord.)25 b(Th)o(e)17 b(14rst)g(10)f(bit)o(s)h((or)f(an)o(y)
  839. g(part)o(icular)g(10)f(bit)o(s))i(of)f(an)0 871 y(in)o(t)o(eger)d(pro)
  840. q(d)o(u)o(ce)q(d)g(b)o(y)g(a)f(gen)o(era)o(t)o(or)i((monk)o(ey))d(d)o
  841. (et)o(ermin)o(e)q(s)i(t)n(h)o(e)h(k)o(eystrok)o(e.)k((W)m(e)12
  842. b(a)o(ban)o(don)g(t)n(h)o(e)h(26-let)n(t)o(er)0 921 y(alph)o(a)o(b)q
  843. (et)g(f)q(rom)f(h)o(ere)j(on;)e(alph)o(a)o(b)q(et)o(s)h(of)f(s)q(ize)h
  844. (2)p Fg(;)7 b Fl(2)798 906 y Fh(2)816 921 y Fg(;)g Fl(2)856
  845. 906 y Fh(3)874 921 y Fg(;)g(:)g(:)g(:)t(;)g Fl(2)987
  846. 906 y Fh(10)1036 921 y Fl(are)14 b(b)q(et)n(t)o(er)h(suit)o(e)q(d)g
  847. (for)e(t)o(e)q(st)o(in)o(g)i(RNG's.))62 971 y(Before)i(d)o(ev)o(elo)o
  848. (pin)o(g)g(t)n(h)o(e)g(t)n(h)o(eory)m(,)f(h)o(ere)h(i)q(s)f(an)g
  849. (example)f(of)g(t)n(h)o(e)i(OPSO)g(t)o(e)q(st:)24 b(W)m(e)16
  850. b(gen)o(era)o(t)o(e)h(2)1584 956 y Fh(21)1635 971 y Fl(k)o(ey-)0
  851. 1020 y(strok)o(e)q(s)j(f)q(rom)c(an)i(alph)o(a)o(b)q(et)f(of)h(2)556
  852. 1005 y Fh(10)610 1020 y Fl(=)h(1024)e(let)n(t)o(ers.)33
  853. b(Eac)o(h)19 b(k)o(eystrok)o(e)g(i)q(s)f(pro)q(d)o(u)o(ce)q(d)h(b)o(y)f
  854. (t)n(h)o(e)h(14rst)g(10)0 1070 y(bit)o(s)d(of)f(t)n(h)o(e)i(con)o
  855. (gruen)o(t)o(ial)e(gen)o(era)o(t)o(or)i Fg(x)646 1076
  856. y Fd(n)683 1070 y Fl(=)e(69069)p Fg(x)859 1076 y Fd(n)p
  857. Fe(00)p Fh(1)934 1070 y Fl(mo)q(d)10 b(2)1046 1055
  858. y Fh(32)1081 1070 y Fl(.)23 b(W)m(e)16 b(cou)o(n)o(t)g(t)n(h)o(e)g(n)n
  859. (u)o(m)n(b)q(er)g(of)f(mi)q(ss)q(in)o(g)0 1120 y(2-let)n(t)o(er)h(w)o
  860. (ords.)21 b(As)16 b(w)o(e)f(sh)o(all)f(s)q(ee,)h(t)n(h)o(e)h(n)n(u)o(m)
  861. n(b)q(er)f(of)f(mi)q(ss)q(in)o(g)f(2-let)n(t)o(er)j(w)o(ords)f(sh)o
  862. (ould)g(b)q(e)g(ap)o(pro)o(xim)o(a)o(t)o(ely)0 1170 y(norm)o(al)9
  863. b(wit)n(h)i Fg(26)h Fl(=)g(141909)d(an)o(d)i Fg(33)i
  864. Fl(=)f(290.)k((T)m(o)11 b(b)q(e)g(more)f(preci)q(s)q(e,)i(in)f(spars)q
  865. (e-o)q(ccupancy)i(t)o(e)q(st)o(s)h(w)o(e)d(exp)q(ect)0
  866. 1220 y(asympt)o(ot)o(ic)i(P)o(oi)q(sson)h(di)q(str)q(ibu)o(t)o(ions)g
  867. (for)g(empt)o(y-cell)f(cou)o(n)o(t)o(s.)21 b(In)14 b(pract)o(ice,)h(t)n
  868. (h)o(a)o(t)f(i)q(s)g(equiv)n(alen)o(t)g(t)o(o)g(us)q(in)o(g)0
  869. 1270 y(a)e(norm)o(al)f(di)q(str)q(ibu)o(t)o(ion,)g(if)h
  870. Fg(25)h Fl(i)q(s)f(large.)17 b(An)o(d)c(exp)q(er)q(ience)h(sh)o(o)o
  871. (ws)f(t)n(h)o(a)o(t)f(ev)o(en)i(wh)o(en)f(n)f(i)q(s)g(not)h(large)f
  872. (enough)0 1319 y(t)o(o)17 b(pro)o(vid)o(e)g(a)g(go)q(o)q(d)f(P)o(oi)q
  873. (sson)h(di)q(str)q(ibu)o(t)o(ion,)g(t)n(h)o(e)g(norm)o(al)e(di)q(str)q
  874. (ibu)o(t)o(ion)h(st)o(ill)g(ap)o(plie)q(s.)27 b(It)17
  875. b(just)g(h)o(ap)o(p)q(ens)0 1369 y(t)n(h)o(a)o(t)d(t)n(h)o(e)h(v)n(ar)q
  876. (iance)e(i)q(s)g(not)h(y)o(et)g(equal)g(t)o(o)g(t)n(h)o(e)h(m)o(ean,)d
  877. (as)i(i)q(s)f(require)q(d)i(in)f(t)n(h)o(e)g(limit.))62
  878. 1419 y(Our)e(14rst)h(ru)o(n)f((wit)n(h)g(s)q(ee)q(d)h(v)n(alue)e
  879. (1234567))f(of)g(2)842 1404 y Fh(21)889 1419 y Fl(k)o(eystrok)o(e)q(s)
  880. j(h)o(as)e(141,979)f(mi)q(ss)q(in)o(g)g(2-let)n(t)o(er)i(w)o(ords,)0
  881. 1469 y(corre)q(sp)q(on)o(din)o(g)j(t)o(o)e(a)g(st)o(an)o(d)o(ard)h
  882. (norm)o(al)d(v)n(ar)q(ia)o(t)o(e)h(of)g(.240.)17 b(Th)o(e)c(n)o(ext)h
  883. (t)n(hree)h(ru)o(ns)f(of)f(2)1381 1454 y Fh(21)1429 1469
  884. y Fl(k)o(eystrok)o(e)q(s)h(h)o(a)o(v)o(e)0 1519 y(141980,)j(141753)f
  885. (an)o(d)h(141785)f(mi)q(ss)q(in)o(g)g(2-let)n(t)o(er)j(w)o(ords,)f
  886. (corre)q(sp)q(on)o(din)o(g)h(t)o(o)f(st)o(an)o(d)o(ard)g(norm)o(al)e(v)
  887. n(alue)q(s)0 1568 y(.243,)c(-.535,)g(-.428.)17 b(Go)q(o)q(d.)g(Our)e
  888. (69069)d(con)o(gruen)o(t)o(ial)i(monk)o(ey)e(com)o(e)q(s)i(t)n(hrough)g
  889. (again.)62 1618 y(No)o(w)i(let's)f(pu)o(t)h(t)n(h)o(e)h(31-bit)d
  890. (left-28-r)q(igh)o(t-3)g(shift-regi)q(st)o(er)i(monk)o(ey)e(a)o(t)h(t)n
  891. (h)o(e)h(k)o(eyb)q(oard.)24 b(W)m(e)15 b(already)0 1668
  892. y(saw)f(h)o(e)g(couldn't)f(m)o(an)o(age)f(CA)m(T)h(on)g(a)h(26-k)o(ey)f
  893. (t)o(yp)q(ewr)q(it)o(er;)g(h)o(o)o(w)g(will)f(h)o(e)i(do)g(on)f(a)g(v)o
  894. (er)q(it)o(a)o(ble)g(organ)g(wit)n(h)0 1718 y(1024)e(k)o(eys?)17
  895. b(Lousy!)h(Wit)n(h)11 b(a)g(s)q(ee)q(d)i(v)n(alue)e(of)g(1234567,)e(hi)
  896. q(s)j(14rst)g(str)q(in)o(g)g(of)f(2)1219 1703 y Fh(21)1265
  897. 1718 y Fl(k)o(eystrok)o(e)q(s)i(h)o(ad)f(1,032,192)0
  898. 1768 y(mi)q(ss)q(in)o(g)g(2-let)n(t)o(er)j(w)o(ords,)f(som)o(e)e(3070)h
  899. (s)q(igm)o(as)f(f)q(rom)g(t)n(h)o(e)j(m)o(ean.)i(Th)o(e)d(s)q(econ)o(d)
  900. g(w)o(as)g(as)g(bad.)62 1818 y(Next,)d(let's)f(imp)q(ort)e(a)i(monk)o
  901. (ey)e(f)q(rom)g(Ber)o(k)o(eley)m(,)k(wit)n(h)d(k)o(eystrok)o(e)q(s)j(d)
  902. o(et)o(ermin)o(e)q(d)e(b)o(y)g(t)n(h)o(e)g(leadin)o(g)g(10)f(bit)o(s)0
  903. 1867 y(f)q(rom)h(t)n(h)o(e)j(Ber)o(k)o(eley)i(Unix)c(RNG)h
  904. Fg(x)562 1873 y Fd(n)596 1867 y Fl(=)g(62605)p Fg(x)769
  905. 1873 y Fd(n)p Fe(00)p Fh(1)838 1867 y Fl(+)6 b(113218009)k(mo)q(d)g
  906. (2)1187 1852 y Fh(29)1222 1867 y Fl(.)18 b(Again)11 b(wit)n(h)i(s)q(ee)
  907. q(d)g(1234567,)0 1917 y(s)q(ix)g(ru)o(ns)j(of)d(2)225
  908. 1902 y Fh(21)274 1917 y Fl(k)o(eystrok)o(e)q(s)i(pro)q(d)o(u)o(ce)q(d)h
  909. (wh)o(a)o(t)d(sh)o(ould)h(b)q(e)g(t)n(h)o(e)h(equiv)n(alen)o(t)e(of)h
  910. (s)q(ix)f(in)o(d)o(ep)q(en)o(d)o(en)o(t)i(st)o(an)o(d)o(ard)0
  911. 1967 y(norm)o(al)f(v)n(alue)q(s:)21 b(-1.771,-3.447,)o(-1.)o(585)o
  912. (,-2.)o(903)o(,-1.)o(757)o(,-2)o(.37)o(0.)g(Not)15 b(go)q(o)q(d;)h(t)n
  913. (hi)q(s)g(Ber)o(k)o(eley)h(monk)o(ey)e(f)q(ails)0 2017
  914. y(t)n(h)o(e)g(OPSO)f(t)o(e)q(st,)h(bu)o(t)f(it)g(i)q(s)f(not)h(t)n(h)o
  915. (e)h(sp)q(ect)o(acular)f(f)q(ailure)f(of)g(t)n(h)o(e)i(shift-regi)q(st)
  916. o(er)f(monk)o(ey)m(.)62 2067 y(Anot)n(h)o(er)k(shift-regi)q(st)o(er)f
  917. (monk)o(ey:)22 b(left)16 b(shift)g(18,)h(r)q(igh)o(t)e(shift)i(13)f(on)
  918. g(31)g(bit)g(w)o(ords.)26 b(Thi)q(s)16 b(monk)o(ey)0
  919. 2116 y(us)q(e)q(s)g(wh)o(a)o(t)e(I)g(h)o(a)o(v)o(e)g(fou)o(n)o(d)g(t)o
  920. (o)h(b)q(e)g(t)n(h)o(e)g(b)q(e)q(st)g(of)f(t)n(h)o(e)h((t)o(w)o
  921. (o-shift))f(shift-regi)q(st)o(er)h(gen)o(era)o(t)o(ors.)21
  922. b(Ho)o(w)14 b(will)f(sh)o(e)0 2166 y(do)h(on)g(OPSO?)h(Wit)n(h)f(s)q
  923. (ee)q(d)i(v)n(alue)e(1234567,)e(our)i(monk)o(ey)f(pro)o(vid)o(e)q(s)i
  924. (2)1158 2151 y Fh(21)1208 2166 y Fl(k)o(eystrok)o(e)q(s)h((f)q(rom)c
  925. (leadin)o(g)i(10)0 2216 y(bit)o(s))h(t)n(h)o(a)o(t)f(h)o(a)o(v)o(e)g
  926. (139,375)f(mi)q(ss)q(in)o(g)f(2-let)n(t)o(er)k(w)o(ords.)j(Th)o(a)o(t)
  927. 14 b(i)q(s)g(-8.74)f(s)q(igm)o(as)f(f)q(rom)h(t)n(h)o(e)i(m)o(ean.)j
  928. (Bad.)i(Th)o(e)0 2266 y(n)o(ext)e(ru)o(n)h(of)e(2)248
  929. 2251 y Fh(21)300 2266 y Fl(k)o(eystrok)o(e)q(s)i(h)o(as)f(139,946)e(mi)
  930. q(ss)q(in)o(g)g(2-let)n(t)o(er)j(w)o(ords:)26 b(-6.77)16
  931. b(s)q(igm)o(as)f(of)j(290)f(f)q(rom)e(t)n(h)o(e)0 2316
  932. y(m)o(ean)e(of)h(141,909.)j(Ev)o(en)e(t)n(h)o(e)g(b)q(e)q(st)g(of)e(t)n
  933. (h)o(e)i(shift-regi)q(st)o(er)g(gen)o(era)o(t)o(ors)h(f)q(ails)c(t)n(h)
  934. o(e)j(OPSO)g(t)o(e)q(st,)g(bu)o(t)g(not)f(in)0 2365 y(as)g(sp)q(ect)o
  935. (acular)h(f)q(ashion)d(as)i(t)n(h)o(os)q(e)h(for)f(ot)n(h)o(er)h(shift)
  936. e(regi)q(st)o(er)i(gen)o(era)o(t)o(ors.)0 2503 y Fi(6)88
  937. b(OPSO)21 b(Th)n(eory)0 2594 y Fl(Th)o(e)f(OPSO)h(t)o(e)q(st)g(cou)o(n)
  938. o(t)o(s)g(t)n(h)o(e)g(n)n(u)o(m)n(b)q(er)f(of)f(mi)q(ss)q(in)o(g)f
  939. (2-let)n(t)o(er)j(w)o(ords)f(in)f(a)h(lon)o(g)f(str)q(in)o(g)i(of)e
  940. Fg(n)h Fl(ran)o(dom)0 2643 y(k)o(eystrok)o(e)q(s.)i(If)14
  941. b Fg(n)f Fl(=)g(2)366 2628 y Fh(21)414 2643 y Fl(=)g(2)p
  942. Fg(;)7 b Fl(097)p Fg(;)g Fl(152)12 b(an)o(d)i(t)n(h)o(ere)i(are)f
  943. Fg(13)e Fl(=)g(2)1016 2628 y Fh(10)1064 2643 y Fl(=)g(1024)h(let)n(t)
  944. o(ers)i(in)e(t)n(h)o(e)i(alph)o(a)o(b)q(et,)d(t)n(h)o(en)0
  945. 2693 y(t)n(h)o(e)i(n)n(u)o(m)n(b)q(er)f(of)g(mi)q(ss)q(in)o(g)f(w)o
  946. (ords)h(sh)o(ould)h(a)o(v)o(erage)f(141,909)f(wit)n(h)h(a)g(st)o(an)o
  947. (d)o(ard)h(d)o(evia)o(t)o(ion)f(of)g(290.)k(Ho)o(w)d(i)q(s)0
  948. 2743 y(t)n(hi)q(s)f(d)o(et)o(ermin)o(e)q(d?)62 2793 y(Th)o(e)k(answ)o
  949. (er:)25 b(not)17 b(eas)q(ily)m(.)27 b(A)o(t)18 b(least,)g(t)n(h)o(e)g
  950. (v)n(ar)q(iance)f(i)q(s)f(not)h(easy;)j(t)n(h)o(e)e(m)o(ean)e
  951. Fk(is)h Fl(easy)m(.)28 b(T)m(o)17 b(get)g(t)n(h)o(e)0
  952. 2843 y(m)o(ean,)f(w)o(e)h(t)o(ak)o(e)g(adv)n(an)o(t)o(age)e(of)i(t)n(h)
  953. o(e)g(n)o(ear)h(lac)o(k-of-m)o(em)o(ory)13 b(pro)o(p)q(ert)o(y)18
  954. b(of)e(t)n(h)o(e)h(monk)o(ey's)e(ou)o(t)o(pu)o(t.)28
  955. b(If)17 b(h)o(e)845 2978 y(3)p eop
  956. %%Page: 4 4
  957. 4 3 bop 0 45 a Fl(h)o(as)16 b(not)h(t)o(yp)q(e)q(d)f(a)g(part)o(icular)
  958. g(w)o(ord)g(aft)o(er,)h(say)m(,)f(1000)f(k)o(eystrok)o(e)q(s,)j(t)n(h)o
  959. (en)f(t)n(h)o(e)g(di)q(str)q(ibu)o(t)o(ion)f(of)g(t)n(h)o(e)h(t)o(im)o
  960. (e)0 95 y(rem)o(ainin)o(g)c(u)o(n)o(t)o(il)g(h)o(e)i(do)q(e)q(s)f(h)o
  961. (as)h(virt)o(ually)d(t)n(h)o(e)j(sam)o(e)f(di)q(str)q(ibu)o(t)o(ion)f
  962. (as)h(t)n(h)o(e)i(or)q(igin)o(al.)h(In)d(ot)n(h)o(er)h(w)o(ords,)f(t)n
  963. (h)o(e)0 145 y(t)o(im)o(e)c(u)o(n)o(t)o(il)g(t)n(h)o(e)i(monk)o(ey)e(t)
  964. o(yp)q(e)q(s)h(a)g(part)o(icular)g(2-let)n(t)o(er)h(w)o(ord)f(sh)o
  965. (ould)g(b)q(e)h(clos)q(e)g(t)o(o)f(exp)q(on)o(en)o(t)o(ial,)g(wit)n(h)g
  966. (m)o(ean)0 195 y Fg(26)16 b Fl(=)h Fg(13)117 179
  967. y Fh(2)152 195 y Fl(=)g(2)222 179 y Fh(20)257 195 y Fl(,)g(an)o(d)f(t)n
  968. (h)o(e)i(proba)o(bilit)o(y)d(h)o(e)i(do)q(e)q(s)g(not)g(t)o(yp)q(e)g(t)
  969. n(h)o(e)g(w)o(ord)g(wit)n(hin)f Fg(n)h Fl(k)o(eystrok)o(e)q(s)h(sh)o
  970. (ould)f(b)q(e)0 244 y Fg(e)19 229 y Fe(00)p Fd(n=26)105
  971. 244 y Fl(,)c(t)o(o)i(cons)q(id)o(era)o(ble)f(accuracy)m(.)62
  972. 294 y(T)m(o)e(d)o(et)o(ermin)o(e)h(t)n(h)o(a)o(t)g(accuracy)m(,)g(w)o
  973. (e)g(n)o(ee)q(d)h(t)n(h)o(e)f(true)h(proba)o(bilit)o(y)d(t)n(h)o(a)o(t)
  974. h Fg(n)h Fl(k)o(eystrok)o(e)q(s)h(will)d(not)i(pro)q(d)o(u)o(ce)0
  975. 344 y(a)h(part)o(icular)f(2-let)n(t)o(er)i(w)o(ord.)i(Th)o(ere)f(are)e
  976. (t)o(w)o(o)f(kin)o(ds)h(of)f(2-let)n(t)o(er)i(w)o(ords:)j(AB)c(an)o(d)g
  977. (AA.)g(Th)o(e)g(proba)o(bilit)o(y)0 394 y(of)f(no)h(AB)g(in)g
  978. Fg(n)f Fl(k)o(eystrok)o(e)q(s)j(i)q(s)305 502 y(t)n(h)o(e)f(co)q
  979. (e16cien)o(t)f(of)f Fg(z)635 487 y Fd(n)672 502 y Fl(in)g(t)n(h)o(e)i
  980. (T)m(aylor)d(expans)q(ion)i(of)1267 474 y(1)p 1166 493
  981. 223 2 v 1166 531 a(1)9 b Ff(00)g Fg(z)j Fl(+)d Fg(p)1330
  982. 519 y Fh(2)1349 531 y Fg(z)1370 519 y Fh(2)1393 502 y
  983. Fg(;)0 618 y Fl(wh)o(ere)15 b Fg(p)c Fl(=)h(2)216 603
  984. y Fe(00)p Fh(10)277 618 y Fl(,)i(t)n(h)o(e)g(proba)o(bilit)o(y)e(for)
  985. i(eac)o(h)h(of)e(t)n(h)o(e)i(k)o(eystrok)o(e)q(s.)62
  986. 668 y(Th)o(e)10 b(gen)o(eral)g(form)d(of)i(t)n(h)o(e)h(require)q(d)h
  987. (proba)o(bilit)o(y)c(i)q(s)i Fg(c)902 674 y Fh(1)921
  988. 668 y Fg(r)941 653 y Fd(n)940 678 y Fh(1)963 668 y Fl(+)p
  989. Fg(c)1013 674 y Fh(2)1033 668 y Fg(r)1053 653 y Fd(n)1052
  990. 678 y Fh(2)1075 668 y Fl(,)h(wit)n(h)f Fg(r)1204 674
  991. y Fh(1)1223 668 y Fg(;)e(r)1261 674 y Fh(2)1288 668 y
  992. Fl(t)n(h)o(e)j(ro)q(ot)o(s)g(of)f Fg(x)1519 653 y Fh(2)1538
  993. 668 y Ff(00)p Fg(x)p Fl(+)p Fg(p)1647 653 y Fh(2)1678
  994. 668 y Fl(=)0 718 y(0)i(an)o(d)g Fg(c)127 724 y Fd(i)152
  995. 718 y Fl(=)h(1)p Fg(=)p Fl(()p Fg(r)273 724 y Fd(i)289
  996. 718 y Ff(00)t Fl(2()p Fg(pr)402 724 y Fd(i)416 718
  997. y Fl())432 703 y Fh(2)450 718 y Fl().)18 b(Ev)o(en)11
  998. b(wit)n(h)g Fg(n)g Fl(as)g(sm)o(all)e(as)i(100)g(t)n(hi)q(s)g(b)q(ecom)
  999. o(e)q(s,)f(t)o(o)i(s)q(ev)o(eral)f(h)n(u)o(n)o(dre)q(d)i(place)q(s,)0
  1000. 768 y Fg(c)18 774 y Fh(1)37 768 y Fg(r)57 753 y Fd(n)56
  1001. 778 y Fh(1)79 768 y Fl(,)g(wit)n(h)h Fg(r)216 774 y Fh(1)248
  1002. 768 y Fl(t)n(h)o(e)h(domin)o(an)o(t)d(ro)q(ot:)73 859
  1003. y(Pr)q((no)i(AB)g(in)f Fg(n)h Fl(strok)o(e)q(s)r())d(=)h(1)p
  1004. Fg(:)p Fl(000002861032)o(0441)o(96()p Fg(:)p Fl(9)o(9999)o(9046)o
  1005. (3247)o(7409)o(7313)o(4994)o(5987)o())1605 842 y Fd(n)1625
  1006. 859 y Fg(:)0 950 y Fl(Wh)o(en)i Fg(n)d Fl(=)h(2)221 935
  1007. y Fh(21)270 950 y Fl(t)n(hi)q(s)i(b)q(ecom)o(e)q(s)f(.13533528323646)o
  1008. (9,)e(compare)q(d)i(t)o(o)h Fg(e)1122 935 y Fe(00)p
  1009. Fh(2)1178 950 y Fl(=)e Fg(:)p Fl(13533528323661)o(2.)62
  1010. 1000 y((I)17 b(am)d(in)o(d)o(e)o(bt)o(e)q(d)k(t)o(o)e(Profe)q(ssor)i
  1011. (Kn)n(u)o(t)n(h)g(for)e(p)q(oin)o(t)o(in)o(g)f(ou)o(t)i(t)n(h)o(e)g(or)
  1012. q(igin)o(al)d(v)o(ers)q(ion)i(h)o(ad)g(an)g(error)i(t)n(h)o(a)o(t)0
  1013. 1050 y(re)q(sul)o(t)o(e)q(d)e(in)d(only)g(7-place)g(accuracy)m(,)h(ra)o
  1014. (t)n(h)o(er)h(t)n(h)o(an)f(t)n(h)o(e)h(13-place)e(accuracy)i(re)q(sul)o
  1015. (t)o(in)o(g)g(f)q(rom)d(hi)q(s)h(14x.))62 1100 y(Th)o(e)h(proba)o
  1016. (bilit)o(y)f(of)g(no)h(AA)g(in)f Fg(n)h Fl(k)o(eystrok)o(e)q(s)h(i)q(s)
  1017. e(di13eren)o(t:)191 1208 y(t)n(h)o(e)h(co)q(e16cien)o(t)g(of)g
  1018. Fg(z)521 1193 y Fd(n)557 1208 y Fl(in)g(t)n(h)o(e)g(T)m(aylor)f(expans)
  1019. q(ion)g(of)1220 1180 y(1)c(+)h Fg(pz)p 1052 1199 452
  1020. 2 v 1052 1237 a Fl(1)e Ff(00)i Fl((1)f Ff(00)h Fg(p)p
  1021. Fl())p Fg(z)h Ff(00)f Fl(()p Fg(p)f Ff(00)g Fg(p)1428
  1022. 1225 y Fh(2)1447 1237 y Fl())p Fg(z)1484 1225 y Fh(2)1508
  1023. 1208 y Fg(:)0 1322 y Fl(F)m(or)k(large)h Fg(n)p Fl(,)f(t)n(hi)q(s)h(b)q
  1024. (ecom)o(e)q(s)41 1413 y(Pr)q((no)g(AA)g(in)f Fg(n)h
  1025. Fl(strok)o(e)q(s)q())e(=)g(1)p Fg(:)p Fl(00000095181)o(7114)o(0532)o
  1026. (98()p Fg(:)p Fl(9)o(9999)o(9047)o(2551)o(9072)o(3887)o(1014)o(2577)o
  1027. ())1637 1396 y Fd(n)1657 1413 y Fg(:)0 1504 y Fl(Wh)o(en)17
  1028. b Fg(n)g Fl(=)g(2)235 1489 y Fh(21)286 1504 y Fl(t)n(hi)q(s)g(b)q(ecom)
  1029. o(e)q(s)g(.1355993519979)o(8659)o(6411)o(.)25 b(Th)o(e)17
  1030. b(lac)o(k-of-m)o(em)o(ory)d(ap)o(pro)o(xim)o(a)o(t)o(ion)g(i)q(s)0
  1031. 1554 y(st)o(ill)f(go)q(o)q(d,)g(bu)o(t)h(not)g(as)g(go)q(o)q(d)g(as)g
  1032. (for)f(w)o(ords)h(AB,)g(o)o(win)o(g)f(t)o(o)i(t)n(h)o(e)f(sp)q(ecial)g
  1033. (n)o(a)o(t)o(ure)g(of)f(w)o(ords)i(AA.)62 1604 y(No)o(w,)f(t)o(o)h
  1034. (14n)o(d)g(t)n(h)o(e)h(exp)q(ect)o(e)q(d)g(n)n(u)o(m)n(b)q(er)e(of)h
  1035. (mi)q(ss)q(in)o(g)e(2-let)n(t)o(er)i(w)o(ords)g(in)f(a)h(str)q(in)o(g)g
  1036. (of)f Fg(n)h Fl(k)o(eystrok)o(e)q(s,)h(w)o(e)0 1654 y(us)q(e)f(in)o
  1037. (dica)o(t)o(or)e(v)n(ar)q(ia)o(ble)q(s.)j(Let)f Fg(w)538
  1038. 1660 y Fh(1)556 1654 y Fg(;)7 b(w)605 1660 y Fh(2)623
  1039. 1654 y Fg(;)g(:)g(:)g(:)e(;)i(w)746 1660 y Fh(209715)o(2)877
  1040. 1654 y Fl(b)q(e)14 b(t)n(h)o(e)g(s)q(et)h(of)e(p)q(oss)q(ible)h(2-let)n
  1041. (t)o(er)h(w)o(ords)f(an)o(d)g(let)488 1745 y Fg(x)512
  1042. 1751 y Fd(i)537 1745 y Fl(=)e(1)i(if)f(w)o(ord)h Fg(w)787
  1043. 1751 y Fd(i)814 1745 y Fl(i)q(s)f(mi)q(ss)q(in)o(g,)f(els)q(e)i
  1044. Fg(x)1120 1751 y Fd(i)1146 1745 y Fl(=)d(0)p Fg(:)0 1837
  1045. y Fl(Th)o(en)k(t)n(h)o(e)h(n)n(u)o(m)n(b)q(er)f(of)f(mi)q(ss)q(in)o(g)f
  1046. (w)o(ords)i(i)q(s)g Fg(x)714 1843 y Fh(1)742 1837 y Fl(+)10
  1047. b Ff(01)d(01)g(01)i Fl(+)h Fg(x)909 1843 y Fh(2097152)1026
  1048. 1837 y Fl(,)15 b(an)o(d)g(t)n(h)o(e)g(exp)q(ect)o(e)q(d)i(n)n(u)o(m)n
  1049. (b)q(er)d(of)h(mi)q(ss)q(in)o(g)0 1886 y(w)o(ords)f(i)q(s)622
  1050. 1936 y(E()p Fg(x)690 1942 y Fh(1)709 1936 y Fl())9
  1051. b(+)g Ff(01)e(01)g(01)h Fl(+)i(E()p Fg(x)943 1942
  1052. y Fh(2097152)1061 1936 y Fl())p Fg(:)62 2011 y Fl(Th)o(ere)19
  1053. b(are)f(2)279 1996 y Fh(20)326 2011 y Ff(00)12 b Fl(2)391
  1054. 1996 y Fh(10)444 2011 y Fl(2-let)n(t)o(er)18 b(w)o(ords)g(of)f(t)o(yp)q
  1055. (e)h(AB,)g(an)o(d)f(2)1055 1996 y Fh(10)1108 2011 y Fl(of)g(t)o(yp)q(e)
  1056. h(AA.)f(Wh)o(en)h Fg(n)g Fl(=)g(2)1585 1996 y Fh(21)1620
  1057. 2011 y Fl(,)g(our)0 2061 y(exp)q(ect)o(e)q(d)d(n)n(u)o(m)n(b)q(er)f(of)
  1058. f(mi)q(ss)q(in)o(g)f(2-let)n(t)o(er)j(w)o(ords)f(i)q(s)263
  1059. 2152 y((2)300 2135 y Fh(20)344 2152 y Ff(00)9 b Fl(2)406
  1060. 2135 y Fh(10)441 2152 y Fl())h Ff(02)f Fg(:)p Fl(13533528323646)o(9)
  1061. d(+)k(2)903 2135 y Fh(10)947 2152 y Ff(02)f Fg(:)p
  1062. Fl(135599351997986)o(5964)o(11)p Fg(;)0 2243 y Fl(an)o(d)14
  1063. b(t)n(hi)q(s)f(re)q(d)o(u)o(ce)q(s)j(t)o(o)e(141909.60)62
  1064. 2293 y(Th)o(e)g(ap)o(pro)o(xim)o(a)o(t)o(ion)d(bas)q(e)q(d)j(on)g(t)n
  1065. (h)o(e)h(lac)o(k-of-m)o(em)o(ory)c(assu)o(mpt)o(ion)i(yields)626
  1066. 2390 y(2)647 2373 y Fh(20)682 2390 y Fg(e)701 2373 y
  1067. Fe(00)p Fh(2)744 2360 y Fb(21)774 2373 y Fd(=)p Fh(2)808
  1068. 2360 y Fb(20)851 2390 y Fl(=)f(141909)p Fg(:)p Fl(33)p
  1069. Fg(:)62 2481 y Fl(Th)n(us)21 b(t)n(h)o(e)g(easy)g(m)o(et)n(h)o(o)q(d)e
  1070. (for)h(14n)o(din)o(g)g(t)n(h)o(e)h(a)o(v)o(erage)f(n)n(u)o(m)n(b)q
  1071. (er)g(of)f(mi)q(ss)q(in)o(g)g(2-let)n(t)o(er)i(w)o(ords)f(f)q(rom)e
  1072. Fg(n)0 2531 y Fl(k)o(eystrok)o(e)q(s,)d(2)234 2516 y
  1073. Fh(20)269 2531 y Fg(e)288 2516 y Fe(00)p Fd(n=)p Fh(2)369
  1074. 2503 y Fb(20)401 2531 y Fl(,)e(i)q(s)g(quit)o(e)h(suit)o(a)o(ble)f(for)
  1075. g(pract)o(ical)h(ap)o(plica)o(t)o(ions)e(of)h(t)n(h)o(e)i(OPSO)f(t)o(e)
  1076. q(st.)62 2581 y(Th)o(os)q(e)j(not)e(acquain)o(t)o(e)q(d)g(wit)n(h)h(m)o
  1077. (et)n(h)o(o)q(ds)f(for)g(d)o(ev)o(elo)o(pin)o(g)g(gen)o(era)o(t)o(in)o
  1078. (g)h(fu)o(nct)o(ions)g(an)o(d)f(solvin)o(g)g(recur-)0
  1079. 2631 y(rence)i(equa)o(t)o(ions)d(su)o(c)o(h)i(as)f(t)n(h)o(os)q(e)h(a)o
  1080. (b)q(o)o(v)o(e)e(m)o(ay)f(wi)q(sh)i(t)o(o)g(lo)q(ok)f(a)o(t)h(t)n(h)o
  1081. (e)g(m)o(arv)o(elous)f(trea)o(t)o(m)o(en)o(t)g(in)h(t)n(h)o(e)g(b)q(o)q
  1082. (ok)0 2681 y([1)o(])j(d)o(ev)o(elo)o(p)q(e)q(d)g(ou)o(t)g(of)f(Don)o
  1083. (ald)g(Kn)n(u)o(t)n(h's)i(concret)o(e)h(m)o(a)o(t)n(h)o(em)o(a)o(t)o(i)
  1084. o(cs)c(cours)q(e)j(a)o(t)f(St)o(anford,)g(in)f(part)o(icular,)0
  1085. 2730 y(s)q(ect)o(ions)e(7.1-7.3)c(an)o(d)j(8.4.)845 2978
  1086. y(4)p eop
  1087. %%Page: 5 5
  1088. 5 4 bop 0 45 a Fa(6.1)56 b(Fin)n(din)o(g)19 b(t)n(h)n(e)f(v)m(ar)q
  1089. (iance)0 122 y Fl(No)o(w)g(for)f(t)n(h)o(e)i(h)o(ard)f(part:)26
  1090. b(t)n(h)o(e)19 b(v)n(ar)q(iance)e(of)g(t)n(h)o(e)i(n)n(u)o(m)n(b)q(er)f
  1091. (of)f(mi)q(ss)q(in)o(g)f(2-let)n(t)o(er)j(w)o(ords.)31
  1092. b(It)18 b(i)q(s)f(t)n(h)o(e)i(su)o(m)0 172 y(of)c(co)o(v()p
  1093. Fg(x)149 178 y Fd(i)163 172 y Fg(;)7 b(x)206 178 y Fd(j)223
  1094. 172 y Fl())16 b(for)f Fg(i)h Fl(an)o(d)g Fg(j)i Fl(eac)o(h)f(ran)o
  1095. (gin)o(g)f(f)q(rom)e(1)h(t)o(o)h(2)924 156 y Fh(10)959
  1096. 172 y Fl(.)24 b((Recall)15 b(t)n(h)o(a)o(t)h Fg(x)1250
  1097. 178 y Fd(i)1280 172 y Fl(i)q(s)f(t)n(h)o(e)i(in)o(dica)o(t)o(or)e(v)n
  1098. (ar)q(ia)o(ble)0 221 y(for)j(t)n(h)o(e)h Fg(i)p Fl(t)n(h)g(w)o(ord,)g
  1099. (1)f(if)g(it)g(ap)o(p)q(ears,)h(0)f(if)g(not).)31 b(Th)o(ere)20
  1100. b(are)f(a)o(b)q(ou)o(t)f(2)1169 206 y Fh(20)1222 221
  1101. y Fl(su)o(c)o(h)h(co)o(v)n(ar)q(iance)q(s)g((act)o(ually)m(,)0
  1102. 271 y(523)12 b Ff(02)h Fl(1023)f(+)h(1024).)34 b(Th)o(ey)19
  1103. b(f)q(all)f(in)o(t)o(o)h(som)o(e)f(17)h(di13eren)o(t)h(t)o(yp)q(e)q
  1104. (s,)h(wit)n(h)e(a)g(gen)o(era)o(t)o(in)o(g)h(fu)o(nct)o(ion)f(for)0
  1105. 321 y(eac)o(h)e(t)o(yp)q(e.)23 b(Th)n(us)17 b(t)n(h)o(e)f(exp)q(ect)o
  1106. (e)q(d)i(v)n(alue)d(of)g Fg(x)744 327 y Fd(i)758 321
  1107. y Fg(x)782 327 y Fd(j)799 321 y Fl(,)g(wit)n(h)h Fg(x)945
  1108. 327 y Fd(i)974 321 y Fl(asso)q(cia)o(t)o(e)q(d)h(wit)n(h)f(a)g(w)o(ord)
  1109. f(su)o(c)o(h)i(as)e(AB,)h(an)o(d)0 371 y Fg(x)24 377
  1110. y Fd(j)56 371 y Fl(asso)q(cia)o(t)o(e)q(d)g(wit)n(h)f(CA,)f(require)q
  1111. (s)i(a)f(di13eren)o(t)h(gen)o(era)o(t)o(in)o(g)f(fu)o(nct)o(ion)g(t)n
  1112. (h)o(an)g(do)q(e)q(s)g(t)n(h)o(a)o(t)g(asso)q(cia)o(t)o(e)q(d)h(wit)n
  1113. (h)0 421 y(AA,BA.)62 470 y(If)10 b(all)g(t)n(h)o(e)h(di13eren)o(t)g
  1114. (t)o(yp)q(e)q(s,)h(an)o(d)e(t)n(h)o(e)q(ir)h(f)q(requencie)q(s,)h(are)f
  1115. (accou)o(n)o(t)o(e)q(d)h(for,)e(t)n(h)o(e)h(t)o(ot)o(al)f(yields)h(t)n
  1116. (h)o(e)g(require)q(d)0 520 y(v)n(ar)q(iance.)17 b(It)11
  1117. b(i)q(s)f(84368.)16 b(Th)n(us,)c(wit)n(h)f(an)f(alph)o(a)o(b)q(et)g(of)
  1118. h(2)883 505 y Fh(10)929 520 y Fl(let)n(t)o(ers,)i(t)n(h)o(e)e(n)n(u)o
  1119. (m)n(b)q(er)g(of)g(mi)q(ss)q(in)o(g)e(2-let)n(t)o(er)j(w)o(ords)0
  1120. 570 y(in)k(a)h(str)q(in)o(g)g(of)f(2)281 555 y Fh(21)333
  1121. 570 y Fl(k)o(eystrok)o(e)q(s)i(h)o(as)f(m)o(ean)f(141,909)f(an)o(d)h
  1122. (st)o(an)o(d)o(ard)i(d)o(evia)o(t)o(ion)e(290.46.)25
  1123. b(It)17 b(ap)o(p)q(ears)h(t)o(o)0 620 y(h)o(a)o(v)o(e)12
  1124. b(a)f(di)q(str)q(ibu)o(t)o(ion)g(clos)q(e)i(enough)f(t)o(o)h(norm)o(al)
  1125. d(t)n(h)o(a)o(t)i(t)n(h)o(e)g(st)o(a)o(t)o(i)q(st)o(ic)g(()p
  1126. Fg(x)5 b Ff(00)g Fl(141909))p Fg(=)p Fl(290)11 b(i)q(s)g(t)n(h)o(e)i
  1127. (ap)o(pro)o(pr)q(ia)o(t)o(e)0 670 y(on)o(e)g(for)f(t)n(h)o(e)i(OPSO)f
  1128. (t)o(e)q(st,)h(wh)o(ere)g Fg(x)e Fl(i)q(s)g(t)n(h)o(e)i(n)n(u)o(m)n(b)q
  1129. (er)e(of)g(2-let)n(t)o(er)i(w)o(ords)f(t)n(h)o(a)o(t)g(are)g(mi)q(ss)q
  1130. (in)o(g)e(f)q(rom)f(t)n(h)o(e)k(str)q(in)o(g)0 719 y(of)h(2)70
  1131. 704 y Fh(21)120 719 y Fl(k)o(eystrok)o(e)q(s.)25 b(A)16
  1132. b(v)n(alue)f(of)g(()p Fg(x)10 b Ff(00)h Fl(141909))p
  1133. Fg(=)p Fl(290)i(in)i(a)o(bsolu)o(t)o(e)h(v)n(alue)f(grea)o(t)o(er)i(t)n
  1134. (h)o(an,)e(say)m(,)g(3)h(i)q(s)f(ca)n(us)q(e)0 769 y(for)e(concer)q(n.)
  1135. 19 b(A)13 b(really)g(go)q(o)q(d)f(monk)o(ey)g((RNG))h(w)o(ould)f(ca)n
  1136. (us)q(e)i(concer)q(n)h(only)d(a)h(few)g(t)o(im)o(e)q(s)f(in)g(1000)g(t)
  1137. o(e)q(st)o(s.)0 907 y Fi(7)88 b(Th)n(e)22 b(OTSO)e(T)-6
  1138. b(e)r(st)0 997 y Fl(OTSO)17 b(m)o(eans)e(Ov)o(erlap)o(pin)o(g-T)m(r)q
  1139. (iple)q(s-Spars)q(e-Occupancy)m(,)i(m)o(eanin)o(g)e(t)n(h)o(e)h(n)n(u)o
  1140. (m)n(b)q(er)g(of)g(mi)q(ss)q(in)o(g)e(3-let)n(t)o(er)0
  1141. 1047 y(w)o(ords)h(in)g(a)g(lon)o(g)f(str)q(in)o(g)i(of)e
  1142. Fg(n)h Fl(k)o(eystrok)o(e)q(s.)23 b(Constrain)o(t)o(s)16
  1143. b(on)f(t)n(h)o(e)h(s)q(ize)f(of)g(our)g(bit)g(m)o(ap)e(m)o(ak)o(e)h
  1144. Fg(13)f Fl(=)h(2)1656 1032 y Fh(6)1689 1047 y Fl(a)0
  1145. 1097 y(reason)o(a)o(ble)g(s)q(ize)g(for)g(t)n(h)o(e)g(alph)o(a)o(b)q
  1146. (et,)f(callin)o(g)f(for)i(an)f(array)h(of)f(2)1022 1082
  1147. y Fh(13)1071 1097 y Fl(32-bit)g(w)o(ords)h(t)o(o)g(record)h(t)n(h)o(e)f
  1148. (pre)q(s)q(ence)0 1147 y(or)f(a)o(bs)q(ence)j(of)c(eac)o(h)j(p)q(oss)q
  1149. (ible)f(w)o(ord.)j(Th)o(e)d(RNG)f(monk)o(ey's)f(k)o(eystrok)o(e)i(will)
  1150. e(b)q(e)i(d)o(et)o(ermin)o(e)q(d)f(b)o(y)h(s)q(ix)e(bit)o(s)0
  1151. 1197 y(f)q(rom)h(t)n(h)o(e)i(ran)o(dom)f(in)o(t)o(eger|most)g(oft)o(en)
  1152. h(t)n(h)o(e)g(leadin)o(g)g(s)q(ix,)f(t)n(h)o(e)i(most)e(imp)q(ort)o(an)
  1153. o(t,)f(bit)o(s.)21 b(Bu)o(t)16 b(ev)o(ery)g(s)q(et)0
  1154. 1247 y(of)c(s)q(ix)f(bit)o(s)i(sh)o(ould)f(pro)o(vid)o(e)g(suit)o(a)o
  1155. (bly)f(ran)o(dom)g(an)o(d)h(in)o(d)o(ep)q(en)o(d)o(en)o(t)h(k)o
  1156. (eystrok)o(e)q(s,)g(if)f(w)o(e)g(are)h(t)o(o)f(h)o(a)o(v)o(e)g(a)g
  1157. (truly)0 1296 y(sa)o(t)o(i)q(sf)q(act)o(ory)h(RNG.)62
  1158. 1346 y(So)k(wit)n(h)g(a)g(k)o(eyb)q(oard)h(of)e Fg(13)h
  1159. Fl(=)h(64)e(k)o(eys)i(our)f(RNG)g(monk)o(ey)f(pro)q(d)o(u)o(ce)q(s,)j
  1160. (say)m(,)e Fg(n)g Fl(=)g(2)1470 1331 y Fh(21)1523 1346
  1161. y Fl(k)o(eystrok)o(e)q(s)0 1396 y(an)o(d)d(w)o(e)h(cou)o(n)o(t)g(t)n(h)
  1162. o(e)g(n)n(u)o(m)n(b)q(er)f(of)g(mi)q(ss)q(in)o(g)f(3-let)n(t)o(er)i(w)o
  1163. (ords.)21 b(En)n(u)o(m)o(era)o(t)o(in)o(g)14 b(t)n(h)o(e)h(p)q(oss)q
  1164. (ible)g(kin)o(ds)f(of)g(3-let)n(t)o(er)0 1446 y(w)o(ords:)k(AAA,)12
  1165. b(AAB,)h(ABA,BAA,ABC,)h(w)o(e)f(14n)o(d)g(gen)o(era)o(t)o(in)o(g)g
  1166. (fu)o(nct)o(ions)g(for)f(t)n(h)o(e)i(proba)o(bilit)o(y)d(t)n(h)o(a)o(t)
  1167. i(eac)o(h)0 1496 y(part)o(icular)20 b(t)o(yp)q(e)h(will)e(b)q(e)h(mi)q
  1168. (ss)q(in)o(g)f(in)h Fg(n)h Fl(k)o(eystrok)o(e)q(s,)i(t)o(ak)o(e)e(in)o
  1169. (t)o(o)f(accou)o(n)o(t)h(t)n(h)o(e)q(ir)h(f)q(requencie)q(s.)39
  1170. b(Th)o(a)o(t)0 1545 y(pro)o(vid)o(e)q(s)15 b(t)n(h)o(e)f(true)h(exp)q
  1171. (ect)o(e)q(d)g(n)n(u)o(m)n(b)q(er)f(of)f(mi)q(ss)q(in)o(g)f(3-let)n(t)o
  1172. (er)j(w)o(ords)f(in)g(a)g(str)q(in)o(g)g(of)f(2)1370
  1173. 1530 y Fh(21)1419 1545 y Fl(k)o(eystrok)o(e)q(s.)20 b(It)14
  1174. b(i)q(s)0 1595 y(87.9393.)62 1645 y(Th)o(e)d(v)n(alue)g(t)n(h)o(a)o(t)f
  1175. (re)q(sul)o(t)o(s)j(f)q(rom)c(t)n(h)o(e)j(lac)o(k-of-m)o(em)o(ory)7
  1176. b(assu)o(mpt)o(ion)k(i)q(s)f Fg(13)1191 1630 y Fh(3)1209
  1177. 1645 y Fg(e)1228 1630 y Fe(00)p Fd(n=13)1314 1617
  1178. y Fb(3)1343 1645 y Fl(=)i(2)1408 1630 y Fh(18)1443 1645
  1179. y Fg(e)1462 1630 y Fe(00)p Fh(8)1519 1645 y Fl(=)f(87)p
  1180. Fg(:)p Fl(9395.)0 1695 y(So,)i(once)i(again,)d(t)n(h)o(e)j(ap)o(pro)o
  1181. (xim)o(a)o(t)o(i)o(on)c(i)q(s)i(v)o(ery)i(accura)o(t)o(e.)62
  1182. 1745 y(It)h(i)q(s)g(a)g(formid)o(a)o(ble)d(t)o(ask)j(t)o(o)h(14n)o(d)
  1183. f(t)n(h)o(e)g(exact)h(v)n(ar)q(iance)f(for)f(t)n(h)o(e)i(n)n(u)o(m)n(b)
  1184. q(er)f(of)f(mi)q(ss)q(in)o(g)g(3-let)n(t)o(er)i(w)o(ords)0
  1185. 1795 y(in)i(2)75 1779 y Fh(21)130 1795 y Fl(k)o(eystrok)o(e)q(s.)36
  1186. b(Th)o(ere)21 b(are)f(h)n(u)o(n)o(dre)q(ds)i(of)d(di13eren)o(t)h(w)o
  1187. (ord-t)o(yp)q(e)g(pairs,)g(su)o(c)o(h)g(as)g(ABA,CAB)g(for)0
  1188. 1844 y(example,)11 b(for)j(whic)o(h)f(gen)o(era)o(t)o(in)o(g)h(fu)o
  1189. (nct)o(ions)g(m)n(ust)f(b)q(e)g(fou)o(n)o(d.)18 b(Th)o(en)c(asympt)o
  1190. (ot)o(ic)e(forms)g(m)n(ust)i(b)q(e)f(fou)o(n)o(d)0 1894
  1191. y(an)o(d)f(com)n(bin)o(e)q(d)g(wit)n(h)g(t)n(h)o(e)i(pro)o(p)q(er)f(f)q
  1192. (requencie)q(s)h(t)o(o)f(get)g(t)n(h)o(e)g(true)h(v)n(ar)q(iance.)j(I)
  1193. 12 b(h)o(ad)h(a)f(h)o(alf-h)o(eart)o(e)q(d)h(pro)r(ject)0
  1194. 1944 y(u)o(n)o(d)o(erw)o(ay)f(t)o(o)g(a)n(u)o(t)o(om)o(a)o(t)o(e)e(t)n
  1195. (h)o(e)i(pro)q(ce)q(ss)i(wit)n(h)d(a)g(compu)o(t)o(er)g(program,)f(bu)o
  1196. (t)h(progre)q(ss)q(e)q(d)j(only)c(t)o(o)i(t)n(h)o(e)f(I-t)n(hink-)0
  1197. 1994 y(it-i)q(s-feas)q(ible)h(st)o(age.)62 2044 y(Not)o(e)k(t)n(h)o(a)o
  1198. (t)f(t)n(h)o(e)g(OTSO)h(t)o(e)q(st)g(do)q(e)q(s)g(not)f(require)g(t)n
  1199. (h)o(e)h(true)g(v)n(ar)q(iance.)21 b(On)o(e)16 b(m)o(ay)d(t)o(e)q(st)j
  1200. (t)n(h)o(a)o(t)f(a)g(s)q(et)h(of)e Fg(x)0 2093 y Fl(v)n(alue)q(s,)f(t)n
  1201. (h)o(e)g(n)n(u)o(m)n(b)q(er)g(of)f(mi)q(ss)q(in)o(g)f(3-let)n(t)o(er)j
  1202. (w)o(ords)f(in)g(a)g(str)q(in)o(g)g(of)f(2)1071 2078
  1203. y Fh(21)1119 2093 y Fl(k)o(eystrok)o(e)q(s,)i(com)o(e)q(s)f(f)q(rom)d
  1204. (a)j(norm)o(al)0 2143 y(di)q(str)q(ibu)o(t)o(ion)e(wit)n(h)h(m)o(ean)f
  1205. (87.85)f(wit)n(h)i(a)g(t-t)o(e)q(st,)h(us)q(in)o(g)f(cu)o(m)n(ula)o(t)o
  1206. (iv)o(e)e(e)q(st)o(im)o(a)o(t)o(e)q(s)i(of)f(t)n(h)o(e)i(st)o(an)o(d)o
  1207. (ard)g(d)o(evia)o(t)o(ion)0 2193 y(f)q(rom)d(t)n(h)o(e)j(sample)e(v)n
  1208. (alue)q(s.)17 b(Larger)c(sample)q(s)e(of)h Fg(x)p Fl('s)g(are)g(n)o
  1209. (ece)q(ssary)j(t)o(o)e(e)q(st)o(a)o(bli)q(sh)e(a)i(t)o(e)q(st)g(f)q
  1210. (ailure.)j(Th)o(e)d(t)o(e)q(st)0 2243 y(i)q(s)g(a)h(bit)f(sh)o(arp)q
  1211. (er)i(wh)o(en)f(w)o(e)g(kno)o(w)g(t)n(h)o(e)g(v)n(ar)q(iance.)62
  1212. 2293 y(Here)i(i)q(s)e(a)g(pract)o(ical)g(example)f(of)h(t)n(h)o(e)h
  1213. (OTSO)g(t)o(e)q(st.)21 b(A)15 b(ran)o(dom)e(n)n(u)o(m)n(b)q(er)h(gen)o
  1214. (era)o(t)o(or)h(pro)o(p)q(os)q(e)q(d)h((an)o(d)0 2342
  1215. y(t)o(ou)o(t)o(e)q(d)i(on)f(in)o(t)o(er)q(n)o(et))h(b)o(y)f(Haas)g([2)
  1216. o(],)g(gen)o(era)o(t)o(e)q(s)i(4-digit)c(ordin)o(ary)i(d)o(ecim)o(al)f
  1217. (in)o(t)o(egers.)28 b(Sup)o(p)q(os)q(e)19 b(w)o(e)e(as-)0
  1218. 2392 y(su)o(m)o(e)d(an)h(alph)o(a)o(b)q(et)e(of)h Fg(13)e
  1219. Fl(=)h(100)h(c)o(h)o(aract)o(ers)i(an)o(d)e(let)h(t)n(h)o(e)g(last)g(t)
  1220. o(w)o(o)f(digit)o(s)g(of)g(Haas-gen)o(era)o(t)o(e)q(d)i(n)n(u)o(m)n(b)q
  1221. (ers)0 2442 y(d)o(et)o(ermin)o(e)d(our)h(monk)o(ey's)d(k)o(eystrok)o(e)
  1222. q(s,)k(t)n(h)o(en)f(cons)q(id)o(er)g(3-let)n(t)o(er)g(w)o(ords.)k(If)13
  1223. b(w)o(e)h(let)f(t)n(h)o(e)h(monk)o(ey)e(pro)q(d)o(u)o(ce)0
  1224. 2492 y(2,000,003)k(k)o(eystrok)o(e)q(s,)21 b(an)o(d)e(h)o(ence)h(2)f
  1225. (milli)o(on)d(3-let)n(t)o(er)k(w)o(ords,)g(w)o(e)f(exp)q(ect)h(t)n(h)o
  1226. (ere)g(sh)o(ould)f(b)q(e)g(arou)o(n)o(d)0 2542 y Fg(13)27
  1227. 2527 y Fh(3)45 2542 y Fg(e)64 2527 y Fe(00)p Fh(2000000)p
  1228. Fd(=)p Fh(100)o(00)o(00)353 2542 y Fl(=)12 b(135)p Fg(;)7
  1229. b Fl(335)12 b(mi)q(ss)q(in)o(g)g(3-let)n(t)o(er)i(w)o(ords.)62
  1230. 2592 y(Th)o(e)k(14rst)h(t)n(hree)h(ru)o(ns)f(pro)q(d)o(u)o(ce)q(d)g
  1231. (147,440,)d(t)n(h)o(en)j(147,922,)d(t)n(h)o(en)i(147,691.)28
  1232. b(Th)o(e)q(s)q(e)19 b(s)q(eem)f(som)o(e)e(43)0 2641 y(s)q(igm)o(as)f(f)
  1233. q(rom)f(t)n(h)o(e)k(m)o(ean|v)o(ery)e(bad,)h(as)g(a)f(more)g(ext)o(ens)
  1234. q(iv)o(e)h(t-t)o(e)q(st)h(w)o(ould)e(sh)o(o)o(w.)27 b((An)17
  1235. b(empir)q(ical)d(ap-)0 2691 y(pro)o(xim)o(a)o(t)o(ion)f(for)k(t)n(h)o
  1236. (e)g(v)n(ar)q(iance)f(sugge)q(st)o(s)i Fg(33)f Fl(=)g(283)e(for)h(t)n
  1237. (hi)q(s)h(part)o(icular)f(OTSO)h(t)o(e)q(st.)27 b(Bu)o(t)17
  1238. b(of)f(cours)q(e,)0 2741 y(t)n(h)o(anks)e(t)o(o)g(Goss)q(et)n(t's)i
  1239. (t-t)o(e)q(st,)f(w)o(e)f(can)g(t)o(e)q(st)h(for)e(t)n(h)o(e)i(m)o(ean)e
  1240. (wit)n(h)o(ou)o(t)h(kno)o(win)o(g)f(t)n(h)o(e)i(v)n(ar)q(iance.))845
  1241. 2978 y(5)p eop
  1242. %%Page: 6 6
  1243. 6 5 bop 0 45 a Fi(8)88 b(Th)n(e)22 b(OQSO)e(T)-6 b(e)r(st)0
  1244. 136 y Fl(OQSO)10 b(m)o(eans)f(Ov)o(erlap)o(pin)o(g-Quadruple)q(s-Spars)
  1245. q(e-Occupancy|t)n(h)o(e)j(n)n(u)o(m)n(b)q(er)d(of)g(mi)q(ss)q(in)o(g)e
  1246. (4-let)n(t)o(er)j(w)o(ords)0 186 y(in)16 b(a)g(lon)o(g)g(str)q(in)o(g)g
  1247. (of)g(k)o(eystrok)o(e)q(s.)26 b(W)m(e)16 b(us)q(e)h(an)f(alph)o(a)o(b)q
  1248. (et)f(of)h Fg(13)f Fl(=)h(2)1115 171 y Fh(5)1150 186
  1249. y Fl(let)n(t)o(ers)i(an)o(d)e(a)g(str)q(in)o(g)g(of)g
  1250. Fg(n)f Fl(=)h(2)1675 171 y Fh(21)0 236 y Fl(k)o(eystrok)o(e)q(s.)28
  1251. b(Th)n(us)18 b(s)q(elect)o(in)o(g)g(an)o(y)e(14v)o(e)h(bit)o(s)h(f)q
  1252. (rom)d(t)n(h)o(e)i(in)o(t)o(eger)g(pro)q(d)o(u)o(ce)q(d)h(b)o(y)f(t)n
  1253. (h)o(e)h(RNG)e(pro)o(vid)o(e)q(s)h(t)n(h)o(e)0 285 y(re)q(sul)o(t)o(in)
  1254. o(g)e(k)o(eystrok)o(e)g(for)e(our)h(RNG)f(monk)o(ey)m(.)62
  1255. 335 y(By)j(en)n(u)o(m)o(era)o(t)o(in)o(g)f(t)n(h)o(e)h(p)q(oss)q(ible)g
  1256. (kin)o(ds)f(of)f(4-let)n(t)o(er)j(w)o(ords,)e(14n)o(din)o(g)g(t)n(h)o
  1257. (e)q(ir)h(gen)o(era)o(t)o(in)o(g)g(fu)o(nct)o(ions)f(an)o(d)0
  1258. 385 y(asympt)o(ot)o(ic)g(forms)f(for)i(t)n(h)o(e)h(co)q(e16cien)o(t)o
  1259. (s)g(of)f Fg(z)749 370 y Fd(n)771 385 y Fl(,)g(t)n(h)o(en)h(com)n
  1260. (binin)o(g)d(t)n(h)o(em)i(wit)n(h)g(t)n(h)o(e)g(pro)o(p)q(er)h(f)q
  1261. (requencie)q(s,)0 435 y(t)n(h)o(e)g(true)g(exp)q(ect)o(e)q(d)h(n)n(u)o
  1262. (m)n(b)q(er)e(of)f(mi)q(ss)q(in)o(g)g(4-let)n(t)o(er)i(w)o(ords)f(in)g
  1263. (a)g(str)q(in)o(g)g(of)g Fg(n)f Fl(=)h(2)1321 420 y Fh(21)1372
  1264. 435 y Fl(k)o(eystrok)o(e)q(s)h(m)o(ay)e(b)q(e)0 485 y(fou)o(n)o(d)i(t)o
  1265. (o)g(b)q(et)n(t)o(er)h(t)n(h)o(an)e(40)h(digit)o(s)f(of)g(accuracy)m(.)
  1266. 27 b(T)m(o)16 b(t)n(h)o(e)i(14rst)f(11)f(digit)o(s,)h(it)g(i)q(s)f
  1267. Fg(26)g Fl(=)g(141909)p Fg(:)p Fl(47365)7 b Fg(:)g(:)f(:)s
  1268. Fl(.)0 535 y(Th)o(e)14 b(ap)o(pro)o(xim)o(a)o(t)o(ion)d(bas)q(e)q(d)j
  1269. (on)g(t)n(h)o(e)g(lac)o(k-of-m)o(emo)o(ry)d(pro)o(p)q(ert)o(y)j(yields)
  1270. g(141909.33.)62 584 y(Th)o(e)h(b)q(o)o(x)f(b)q(elo)o(w)f(giv)o(e)q(s)i
  1271. (d)o(et)o(ails)f(of)g(t)n(h)o(a)o(t)g(en)n(u)o(m)o(era)o(t)o(ion:)19
  1272. b(F)m(or)14 b(eac)o(h)h(t)o(yp)q(e)f(of)g(w)o(ord,)g(t)n(h)o(e)h(f)q
  1273. (requency)m(,)f(t)n(h)o(e)0 634 y(gen)o(era)o(t)o(in)o(g)f(fu)o(nct)o
  1274. (ion)g(an)o(d)f(t)n(h)o(e)i(proba)o(bilit)o(y)d(t)n(h)o(a)o(t)h(a)h
  1275. (str)q(in)o(g)g(of)f Fg(n)f Fl(=)h(2)1096 619 y Fh(21)1144
  1276. 634 y Fl(k)o(eystrok)o(e)q(s)i(will)d(not)i(con)o(t)o(ain)f(t)n(h)o(a)o
  1277. (t)0 684 y(w)o(ord.)18 b(Th)o(e)c(not)o(a)o(t)o(ion)f(A)397
  1278. 669 y Fe(0)422 684 y Fl(m)o(eans)h(not-A,)f(X)h(an)o(d)g(Y)g(d)o(e)q(s)
  1279. q(ign)o(a)o(t)o(e)g(an)o(y)f(let)n(t)o(ers)j(of)d(t)n(h)o(e)i(alph)o(a)
  1280. o(b)q(et.)104 775 y(Th)o(e)f(Exp)q(ect)o(e)q(d)h(Nu)o(m)n(b)q(er)f(of)f
  1281. (Mi)q(ss)q(in)o(g)g(W)m(ords)h(f)q(rom)104 825 y(A)g(Str)q(in)o(g)g(of)
  1282. f Fg(n)e Fl(=)h(2)422 810 y Fh(21)471 825 y Fl(4-Let)n(t)o(er)j(W)m
  1283. (ords.)104 875 y(Th)o(e)f(Alph)o(a)o(b)q(et)f(Has)h Fg(13)e
  1284. Fl(=)f(32)j(Let)n(t)o(ers.)104 966 y(F)m(orm)e(of)h(w)o(ord:)18
  1285. b(AXY)m(A)500 951 y Fe(0)512 966 y Fl(,)13 b(()p Fg(13)580
  1286. 951 y Fh(4)608 966 y Ff(00)c Fg(13)676 951 y Fh(3)708
  1287. 966 y Fl(of)14 b(t)n(h)o(e)q(s)q(e))104 1016 y Fg(N)5
  1288. b Fl(()p Fg(z)r Fl())12 b(=)f(1)p Fg(=)p Fl((1)e Ff(00)h
  1289. Fg(z)h Fl(+)e Fg(p)472 1001 y Fh(4)491 1016 y Fg(z)512
  1290. 1001 y Fh(4)531 1016 y Fl())104 1065 y(Domin)o(an)o(t)i(ro)q(ot:)18
  1291. b Fg(r)12 b Fl(=)g Fg(:)p Fl(99999904632295)o(5096)o(63)c
  1292. Ff(30)k Fl(1)d Ff(00)h Fg(p)1052 1050 y Fh(4)1079
  1293. 1065 y Ff(00)g Fl(3)p Fg(p)1163 1050 y Fh(8)104 1115
  1294. y Fl(Co)q(e16cien)o(t:)17 b Fg(c)12 b Fl(=)g(1)p Fg(:)p
  1295. Fl(00000381472)o(2731)o(6674)o(7)d Ff(30)j Fl(1)d(+)g(4)p
  1296. Fg(p)1014 1100 y Fh(4)1042 1115 y Fl(+)g(28)p Fg(p)1146
  1297. 1100 y Fh(8)104 1165 y Fl(Con)o(tr)q(ibu)o(t)o(ion)k(t)o(o)h
  1298. Fg(26)p Fl(:)k(()p Fg(13)499 1150 y Fh(4)527 1165
  1299. y Ff(00)9 b Fg(13)595 1150 y Fh(3)613 1165 y Fl())p
  1300. Fg(cr)667 1150 y Fd(n)701 1165 y Fl(=)j(137474)p Fg(:)p
  1301. Fl(27007432)o(8924)o(16)104 1256 y(F)m(orm)g(of)h(w)o(ord:)18
  1302. b(AXY)m(A,)13 b(wit)n(h)h(XY)g(not)g(AA)g(()p Fg(13)887
  1303. 1241 y Fh(3)915 1256 y Ff(00)9 b Fg(13)14 b Fl(of)f(t)n(h)o(e)q(s)q
  1304. (e))104 1306 y Fg(N)5 b Fl(()p Fg(z)r Fl())12 b(=)f((1)f(+)f
  1305. Fg(p)359 1291 y Fh(3)378 1306 y Fg(z)399 1291 y Fh(3)417
  1306. 1306 y Fl())p Fg(=)p Fl((1)g Ff(00)h Fg(z)h Fl(+)f
  1307. Fg(p)635 1291 y Fh(3)653 1306 y Fg(z)674 1291 y Fh(3)702
  1308. 1306 y Fl(+)g(()p Fg(p)781 1291 y Fh(4)809 1306 y Ff(00)f
  1309. Fg(p)871 1291 y Fh(3)890 1306 y Fl())p Fg(z)927 1291
  1310. y Fh(4)945 1306 y Fl())104 1356 y(Domin)o(an)o(t)i(ro)q(ot:)18
  1311. b Fg(r)12 b Fl(=)g Fg(:)p Fl(99999904635205)o(8288)o(73)c
  1312. Ff(30)k Fl(1)d Ff(00)h Fg(p)1052 1341 y Fh(4)1079
  1313. 1356 y Fl(+)g Fg(p)1142 1341 y Fh(7)104 1406 y Fl(Co)q(e16cien)o(t:)
  1314. 17 b Fg(c)12 b Fl(=)g(1)p Fg(:)p Fl(00000381451)o(9010)o(6827)o(9)d
  1315. Ff(30)j Fl(1)d(+)g(4)p Fg(p)1014 1391 y Fh(4)1042 1406
  1316. y Ff(00)g Fl(7)p Fg(p)1125 1391 y Fh(7)104 1455 y Fl(Con)o(tr)q(ibu)o
  1317. (t)o(ion)k(t)o(o)h Fg(26)p Fl(:)k(()p Fg(13)499
  1318. 1440 y Fh(3)527 1455 y Ff(00)9 b Fg(13)p Fl())p
  1319. Fg(cr)649 1440 y Fd(n)683 1455 y Fl(=)j(4430)p Fg(:)p
  1320. Fl(5935638)o(34475)o(83)104 1547 y(F)m(orm)g(of)h(w)o(ord:)18
  1321. b(AAAA,)c(()p Fg(13)g Fl(of)f(t)n(h)o(e)q(s)q(e))104
  1322. 1596 y Fg(N)5 b Fl(()p Fg(z)r Fl())12 b(=)f((1)c(+)g
  1323. Fg(pz)h Fl(+)f Fg(p)441 1581 y Fh(2)460 1596 y Fg(z)481
  1324. 1581 y Fh(2)506 1596 y Fl(+)g Fg(p)566 1581 y Fh(3)584
  1325. 1596 y Fg(z)605 1581 y Fh(3)624 1596 y Fl())p Fg(=)p
  1326. Fl((1)g Ff(00)g Fl((1)g Ff(00)g Fg(p)p Fl())p
  1327. Fg(z)g Ff(00)g Fl(()p Fg(p)g Ff(00)g Fg(p)1033 1581
  1328. y Fh(2)1051 1596 y Fl())p Fg(z)1088 1581 y Fh(2)1113
  1329. 1596 y Ff(00)g Fl(()p Fg(p)1189 1581 y Fh(2)1214 1596
  1330. y Ff(00)g Fg(p)1274 1581 y Fh(3)1292 1596 y Fl())p
  1331. Fg(z)1329 1581 y Fh(3)1355 1596 y Ff(00)g Fl(()p Fg(p)1431
  1332. 1581 y Fh(3)1456 1596 y Ff(00)g Fg(p)1516 1581 y Fh(4)1534
  1333. 1596 y Fl())p Fg(z)1571 1581 y Fh(4)1590 1596 y Fl())104
  1334. 1646 y(Domin)o(an)o(t)k(ro)q(ot:)18 b Fg(r)12 b Fl(=)g
  1335. Fg(:)p Fl(99999907612459)o(1803)o(097)c Ff(30)k Fl(1)d
  1336. Ff(00)g Fg(p)1072 1631 y Fh(4)1100 1646 y Fl(+)h Fg(p)1163
  1337. 1631 y Fh(5)104 1696 y Fl(Co)q(e16cien)o(t:)17 b Fg(c)12
  1338. b Fl(=)g(1)p Fg(:)p Fl(00000366571)o(6133)o(5900)o(77)c
  1339. Ff(30)k Fl(1)d(+)h Fg(p)1014 1681 y Fh(4)1042 1696
  1340. y Ff(00)f Fl(5)p Fg(p)1125 1681 y Fh(5)104 1746 y Fl(Con)o(tr)q(ibu)o
  1341. (t)o(ion)k(t)o(o)h Fg(26)p Fl(:)k Fg(13cr)521 1731
  1342. y Fd(n)554 1746 y Fl(=)12 b(4)p Fg(:)p Fl(6100168562260)o(0658)o(8130)o
  1343. (7)104 1837 y(T)m(ot)o(al:)k Fg(26)c Fl(=)g(141909)p
  1344. Fg(:)p Fl(47365)104 1887 y(Lac)o(k-of-m)o(em)o(ory)f(ap)o(pro)o(xim)o
  1345. (a)o(t)o(ion:)k Fg(13)726 1872 y Fh(4)744 1887 y Fg(e)763
  1346. 1872 y Fe(00)p Fd(n=13)849 1859 y Fb(4)878 1887 y
  1347. Fl(=)d(141909)p Fg(:)p Fl(33)62 1978 y(I)20 b(don't)f(kno)o(w|an)o(d)g
  1348. (dou)n(bt)h(t)n(h)o(a)o(t)g(I)g(ev)o(er)h(will)d(kno)o(w|t)n(h)o(e)h
  1349. (true)i(v)n(ar)q(iance.)35 b(Th)o(ere)21 b(are)g(just)f(t)o(o)q(o)0
  1350. 2028 y(m)o(an)o(y)10 b(kin)o(ds)h(of)g(pairs)h(of)f(4-let)n(t)o(er)i(w)
  1351. o(ords)e(t)o(o)h(u)o(n)o(d)o(ert)o(ak)o(e)i(14n)o(din)o(g)d(all)f(t)n
  1352. (h)o(e)j(n)o(ece)q(ssary)h(gen)o(era)o(t)o(in)o(g)e(fu)o(nct)o(ions.)0
  1353. 2077 y(Ext)o(ens)q(iv)o(e)j(s)q(im)n(ula)o(t)o(ion)e(sugge)q(st)o(s)k
  1354. (t)n(h)o(a)o(t)e(us)q(in)o(g)g Fg(33)g Fl(=)f(295)g(will)g(s)q(erv)o
  1355. (e)j(w)o(ell)d(for)h(t)o(e)q(st)o(in)o(g)h(a)f(ran)o(dom)e(n)n(u)o(m)n
  1356. (b)q(er)0 2127 y(gen)o(era)o(t)o(or:)18 b(t)n(h)o(e)13
  1357. b(v)n(alue)q(s)g((mi)q(ss)q(in)o(gw)o(ords-141909)/2)o(95)c(sh)o
  1358. (ould)j(lo)q(ok)f(lik)o(e)h(in)o(d)o(ep)q(en)o(d)o(en)o(t)h(st)o(an)o
  1359. (d)o(ard)g(norm)o(al)0 2177 y(v)n(ar)q(ia)o(t)o(e)q(s.)32
  1360. b(Th)o(e)19 b(al)o(t)o(er)q(n)o(a)o(t)o(iv)o(e)f(i)q(s)g(t)o(o)h(t)o
  1361. (ak)o(e)g(a)f(larger)h(sample)e(an)o(d)h(do)h(a)f(t-t)o(e)q(st)i(for)e
  1362. (t)n(h)o(e)i(kno)o(wn)e(m)o(ean)g(of)0 2227 y(141,909.)0
  1363. 2364 y Fi(9)88 b(Th)n(e)22 b(DNA)f(T)-6 b(e)r(st)0 2455
  1364. y Fl(If)11 b(w)o(e)h(h)o(a)o(v)o(e)g(an)f(alph)o(a)o(b)q(et)g(of)g(4)h
  1365. (let)n(t)o(ers:)19 b(C,G,A,T,)9 b(t)n(h)o(en)k(a)e(su)o(cce)q(ss)q(ion)
  1366. j(of)d(k)o(eystrok)o(e)q(s)i(f)q(rom)d(t)n(h)o(a)o(t)i(alph)o(a)o(b)q
  1367. (et)0 2505 y(will)h(lo)q(ok)g(lik)o(e)h(t)n(h)o(e)h(m)o(ap)o(pin)o(g)e
  1368. (of)g(a)h(s)q(egm)o(en)o(t)g(of)g(DNA.)g(Hence)h(t)n(h)o(e)h(n)o(am)o
  1369. (e.)i(Our)d(monk)o(ey)e(gen)o(era)o(t)o(e)q(s)i(lon)o(g)0
  1370. 2555 y(str)q(in)o(gs)j(an)o(d)e(w)o(e)h(lo)q(ok)f(for)h(t)n(h)o(e)g
  1371. (incid)o(ence)h(of)f(10-let)n(t)o(er)g(w)o(ords.)27 b(Th)n(us)18
  1372. b(w)o(e)f(h)o(a)o(v)o(e)f(2)1348 2540 y Fh(20)1400 2555
  1373. y Fl(p)q(oss)q(ible)h(10-let)n(t)o(er)0 2605 y(w)o(ords,)h(an)o(d)e(w)o
  1374. (e)i(n)o(ee)q(d)g(an)f(array)g(of)f(2)627 2589 y Fh(15)679
  1375. 2605 y Fl(32-bit)g(w)o(ords)i(for)e(m)o(ap)o(pin)o(g)f(t)n(h)o(e)j(pre)
  1376. q(s)q(ence)i(or)d(a)o(bs)q(ence)i(of)d(all)0 2654 y(p)q(oss)q(ible)e
  1377. (10-let)n(t)o(er)h(w)o(ords.)62 2704 y(As)d(wit)n(h)e(OTSO)i(an)o(d)e
  1378. (OQSO,)h(w)o(e)g(can)g(14n)o(d)g(t)n(h)o(e)h(exact)f(exp)q(ect)o(e)q
  1379. (d)h(n)n(u)o(m)n(b)q(er)f(of)f(mi)q(ss)q(in)o(g)f(10-let)n(t)o(er)j(w)o
  1380. (ords)0 2754 y(f)q(rom)g(a)h(str)q(in)o(g)i(of,)d(say)m(,)h
  1381. Fg(n)f Fl(=)g(2)493 2739 y Fh(21)541 2754 y Fl(k)o(eystrok)o(e)q(s,)j
  1382. (bu)o(t)g(14n)o(din)o(g)e(t)n(h)o(e)i(exact)g(v)n(ar)q(iance)e(lo)q
  1383. (oks)g(h)o(o)o(p)q(ele)q(ss.)62 2804 y(T)m(o)18 b(14n)o(d)g(t)n(h)o
  1384. (e)h(true)g(exp)q(ect)o(e)q(d)g(n)n(u)o(m)n(b)q(er)f(of)g(mi)q(ss)q(in)
  1385. o(g)e(10-let)n(t)o(er)j(w)o(ords,)g(w)o(e)g(m)n(ust)e(cons)q(id)o(er)j
  1386. (22)d(kin)o(ds)0 2854 y(of)d(10-let)n(t)o(er)h(w)o(ords)g((d)o(ep)q
  1387. (en)o(din)o(g)g(on)f(h)o(o)o(w)g(m)o(an)o(y)e(leadin)o(g)j(s)q(egm)o
  1388. (en)o(t)o(s)f(of)g(eac)o(h)h(w)o(ord)g(m)o(a)o(t)o(c)o(h)e(equal-len)o
  1389. (gt)n(h)845 2978 y(6)p eop
  1390. %%Page: 7 7
  1391. 7 6 bop 0 45 a Fl(trailin)o(g)14 b(s)q(egm)o(en)o(t)o(s),)i(14n)o(d)
  1392. f(t)n(h)o(e)q(ir)h(gen)o(era)o(t)o(in)o(g)g(fu)o(nct)o(ions,)g(t)n(h)o
  1393. (e)g(proba)o(bilit)o(y)d(t)n(h)o(e)j(w)o(ord)g(will)e(not)h(ap)o(p)q
  1394. (ear)g(in)0 95 y Fg(n)c Fl(=)h(2)101 80 y Fh(21)150 95
  1395. y Fl(k)o(eystrok)o(e)q(s,)j(t)n(h)o(en)g(com)n(bin)o(e)d(all)h(t)n(h)o
  1396. (os)q(e)i(proba)o(bilit)o(ie)q(s,)d(wit)n(h)i(ap)o(pro)o(pr)q(ia)o(t)o
  1397. (e)f(f)q(requencie)q(s.)62 145 y(Th)o(e)i(re)q(sul)o(t)h(i)q(s)e
  1398. (141910.5378411)o(,)e(t)n(h)o(e)j(exp)q(ect)o(e)q(d)h(n)n(u)o(m)n(b)q
  1399. (er)e(of)g(mi)q(ss)q(in)o(g)f(10-let)n(t)o(er)i(w)o(ords)g(in)f(a)h
  1400. (ran)o(dom)0 195 y(DNA)c(s)q(egm)o(en)o(t)f(of)h(2)328
  1401. 179 y Fh(21)374 195 y Fl(C's,G's,A's)e(an)o(d)i(T's.)17
  1402. b(Th)o(e)12 b(exp)q(ect)o(e)q(d)g(v)n(alue)f(f)q(rom)e(t)n(h)o(e)j(lac)
  1403. o(k-of-m)o(em)o(o)o(ry)d(pro)o(p)q(ert)o(y)0 244 y(i)q(s)k(t)n(h)o(e)i
  1404. (sam)o(e)e(as)h(t)n(h)o(a)o(t)g(for)f(OPSO)i(an)o(d)f(OQSO,)g(wit)n(h)g
  1405. Fg(13)889 229 y Fd(k)920 244 y Fl(=)e(2)985 229 y Fh(20)1034
  1406. 244 y Fl(an)o(d)i Fg(25)d Fl(=)h(2:)18 b(141909.)62
  1407. 294 y(It)10 b(ap)o(p)q(ears)g(a)g(formid)o(a)o(ble)d(t)o(ask)j(t)o(o)g
  1408. (14n)o(d)f(t)n(h)o(e)i(exact)f(v)n(ar)q(iance)g(for)f(t)n(h)o(e)h
  1409. (DNA)g(t)o(e)q(st.)18 b(A)10 b(t-t)o(e)q(st)g(m)o(ay)e(b)q(e)i(us)q(e)q
  1410. (d)0 344 y(t)o(o)i(t)o(e)q(st)g(t)n(h)o(a)o(t)g(t)n(h)o(e)g(m)o(ean)e
  1411. (i)q(s)h(141,910.)k(It)d(will)e(require)i(a)f(larger)h(sample)d(t)n(h)o
  1412. (an)j(on)o(e)f(us)q(in)o(g)h(t)n(h)o(e)g(true)g(v)n(ar)q(iance.)0
  1413. 394 y(Bu)o(t)j(ext)o(ens)q(iv)o(e)g(s)q(im)n(ula)o(t)o(ion)d(sugge)q
  1414. (st)o(s)k(us)q(e)f(of)f(a)g(s)q(igm)o(a)e(of)i(339.)19
  1415. b(So)14 b(a)h(reason)n(ble)g(implem)n(en)o(t)o(a)o(t)o(i)o(on)c(of)j(t)
  1416. n(h)o(e)0 444 y(DNA)h(t)o(e)q(st)h(i)q(s)f(t)n(hi)q(s:)20
  1417. b(Gen)o(era)o(t)o(e)c(2)530 429 y Fh(21)580 444 y Fl(k)o(eystrok)o(e)q
  1418. (s)h(f)q(rom)c(t)n(h)o(e)j(alph)o(a)o(b)q(et)e Ff(f)p
  1419. Fl(C,G,A,T)p Ff(g)f Fl((us)q(in)o(g)i(t)o(w)o(o)f(bit)o(s)i(f)q(rom)0
  1420. 493 y(eac)o(h)d(ran)o(dom)d(in)o(t)o(eger),)j(an)o(d)f(let)g
  1421. Fg(x)f Fl(b)q(e)i(t)n(h)o(e)f(n)n(u)o(m)n(b)q(er)g(of)g(mi)q(ss)q(in)o
  1422. (g)e(10-let)n(t)o(er)j(w)o(ords.)k(Do)12 b(t)n(hi)q(s,)g(say)g(4,)g(t)o
  1423. (im)o(e)q(s.)0 543 y(Th)o(e)j(re)q(sul)o(t)o(in)o(g)g(v)n(alue)q(s)f
  1424. (()p Fg(x)420 549 y Fh(1)448 543 y Ff(00)c Fl(141911))p
  1425. Fg(=)p Fl(339)p Fg(;)d(:)g(:)f(:)s(;)h Fl(()p Fg(x)846
  1426. 549 y Fh(4)874 543 y Ff(00)j Fl(141911))p Fg(=)p Fl(339))i(sh)o
  1427. (ould)i(lo)q(ok)f(lik)o(e)h(a)g(sample)f(of)g(4)0 593
  1428. y(in)o(d)o(ep)q(en)o(d)o(en)o(t)i(st)o(an)o(d)o(ard)f(norm)o(al)e(v)n
  1429. (ar)q(ia)o(ble)q(s.)0 730 y Fi(10)88 b(Di13erence)r(s)20
  1430. b(in)h(t)m(h)n(e)h(T)-6 b(e)r(st)o(s)0 821 y Fl(Ho)o(w)18
  1431. b(do)f(t)n(h)o(e)i(t)o(e)q(st)o(s)h(OPSO,)e(OTSO,)g(OQSO)h(an)o(d)e
  1432. (DNA)h(di13er?)31 b(All)17 b(of)h(t)n(h)o(em)f(cou)o(n)o(t)h(t)n(h)o
  1433. (e)h(n)n(u)o(m)n(b)q(er)f(of)0 871 y(mi)q(ss)q(in)o(g)13
  1434. b Fg(k)q Fl(-let)n(t)o(er)j(w)o(ords)f(in)f(a)g(lon)o(g)h(str)q(in)o(g)
  1435. g(of)f Fg(n)g Fl(k)o(eystrok)o(e)q(s)j(f)q(rom)12 b(an)j(alph)o(a)o(b)q
  1436. (et)f(of)g Fg(13)g Fl(let)n(t)o(ers,)i(an)o(d)f(t)n(h)n(us)0
  1437. 921 y(t)o(e)q(st)g(b)q(ot)n(h)f(u)o(niformit)o(y)e(an)o(d)h(in)o(d)o
  1438. (ep)q(en)o(d)o(ence)j(in)e(t)n(h)o(e)g(ou)o(t)o(pu)o(t)h(of)f(a)f(ran)o
  1439. (dom)f(n)n(u)o(m)n(b)q(er)i(gen)o(era)o(t)o(or.)62 971
  1440. y(OPSO)f(us)q(e)q(s)h(more)d(of)h(eac)o(h)h(ran)o(dom)e(n)n(u)o(m)n(b)q
  1441. (er,)h(10)g(bit)o(s,)g(bu)o(t)h(space)h(an)o(d)e(t)o(im)o(e)e(limit)o
  1442. (a)o(t)o(io)o(ns)g(only)i(allo)o(w)0 1020 y(t)o(e)q(st)o(in)o(g)i
  1443. (2-let)n(t)o(er)h(w)o(ords,)f(t)n(h)o(a)o(t)g(i)q(s,)e(in)o(d)o(ep)q
  1444. (en)o(d)o(ence)k(for)d(pairs)h((2)g(dim)o(ens)q(ions).)i(On)e(t)n(h)o
  1445. (e)g(ot)n(h)o(er)h(h)o(an)o(d,)e(DNA)0 1070 y(can)f(t)o(e)q(st)h(10-t)o
  1446. (uple)q(s)f((10)f(dim)o(ens)q(ion)o(al)e(b)q(e)o(h)o(a)o(viour))j(bu)
  1447. o(t,)g(again)f(f)q(rom)f(t)o(im)o(e)g(an)o(d)i(space)h(cons)q(id)o(era)
  1448. o(t)o(ions,)f(a)o(t)0 1120 y(a)g(d)o(ept)n(h)h(of)f(only)f(2)h(bit)o(s)
  1449. g(p)q(er)h(ran)o(dom)d(n)n(u)o(m)n(b)q(er.)18 b(Som)o(e)10
  1450. b(RNG's)i(m)o(ay)e(do)i(w)o(ell)f(in)h(on)o(e)g(of)f(t)n(h)o(e)i(t)o(e)
  1451. q(st)o(s)h(an)o(d)e(not)0 1170 y(in)g(t)n(h)o(e)i(ot)n(h)o(er.)19
  1452. b(OTSO)13 b(an)o(d)g(OQSO)g(are)h(in)e(b)q(et)o(w)o(een,)i(us)q(in)o(g)
  1453. e(6)h(bit)o(s)g(f)q(rom)e(eac)o(h)j(n)n(u)o(m)n(b)q(er)f(for)f(b)q(e)o
  1454. (h)o(a)o(viour)g(in)0 1220 y(3)i(dim)o(ens)q(ions)e(or)h(5)h(bit)o(s)h
  1455. (f)q(rom)c(eac)o(h)k(n)n(u)o(m)n(b)q(er)f(for)f(4)h(dim)o(ens)q(ions.)
  1456. 62 1270 y(Of)g(cours)q(e)h(a)f(go)q(o)q(d)g(RNG)f(monk)o(ey)f(sh)o
  1457. (ould)i(pass)h(all)e(t)n(h)o(e)q(s)q(e)i(t)o(e)q(st)o(s.)21
  1458. b(W)m(e)13 b(n)o(ext)i(giv)o(e)e(example)q(s)g(of)g(go)q(o)q(d)0
  1459. 1319 y(an)o(d)h(not)f(so)h(go)q(o)q(d)g(RNG)f(monk)o(eys.)0
  1460. 1457 y Fi(11)88 b(Re)r(sul)o(t)o(s)21 b(of)h(Ext)n(ens)q(iv)n(e)f(Monk)
  1461. n(ey)g(T)-6 b(e)r(st)o(s)0 1548 y Fl(I)15 b(h)o(a)o(v)o(e)h(ap)o(plie)q
  1462. (d)e(v)n(ar)q(ious)g(monk)o(ey)g(t)o(e)q(st)o(s)k(t)o(o)d(m)o(an)o(y)f
  1463. (di13eren)o(t)i(RNG's.)22 b(I)16 b(14n)o(d)f(OPSO,OQSO)i(an)o(d)e
  1464. (DNA)0 1597 y(t)o(o)e(b)q(e)g(t)n(h)o(e)g(most)f(e13ect)o(iv)o(e.)19
  1465. b(Simple)10 b(t)o(e)q(st)o(s)15 b(su)o(c)o(h)e(as)g(t)n(h)o(e)g(CA)m(T)
  1466. g(t)o(e)q(st)g(of)f(Sect)o(ion)h(1)g(are)g(eas)q(ily)f(programm)o(e)q
  1467. (d,)0 1647 y(bu)o(t)17 b(more)f(complica)o(t)o(e)q(d)f(programs)g(su)o
  1468. (c)o(h)i(as)g(t)n(h)o(os)q(e)h(for)e(OPSO,)h(OQSO)h(or)e(DNA)h(are)g
  1469. (really)f(not)h(t)n(h)o(a)o(t)0 1697 y(complica)o(t)o(e)q(d,)10
  1470. b(an)o(d)h(t)n(h)o(e)h(read)o(er)i(m)o(ay)c(14n)o(d)h(it)h(eas)q(ier)
  1471. g(t)o(o)g(program)e(hi)q(s)h(o)o(wn)g(v)o(ers)q(ions)h(ra)o(t)n(h)o(er)
  1472. h(t)n(h)o(an)f(get)g(t)n(h)o(em)0 1747 y(f)q(rom)g(m)o(e)h(an)o(d)g
  1473. (14gure)i(ou)o(t)f(h)o(o)o(w)f(t)o(o)h(us)q(e)h(t)n(h)o(em.)62
  1474. 1797 y(Next,)e(let)f(us)g(sugge)q(st)h(v)n(ar)q(ious)e(lev)o(els)h(of)f
  1475. (str)q(in)o(gency)i(for)f(t)o(e)q(st)o(s)i(of)d(a)h(ran)o(dom)e(n)n(u)o
  1476. (m)n(b)q(er)i(gen)o(era)o(t)o(or.)18 b(F)m(or)0 1846
  1477. y(most)10 b(ap)o(plica)o(t)o(ions,)f(t)n(h)o(e)j(leadin)o(g)e(bit)o(s,)
  1478. i(say)f(t)n(h)o(e)g(t)n(h)o(e)h(14rst)f(10{16)f(bit)o(s,)h(of)g(a)f
  1479. (RNG)g(are)h(t)n(h)o(e)h(most)e(imp)q(ort)o(an)o(t)0
  1480. 1896 y(an)o(d)16 b(sh)o(ould)h(pass)g(all)f(t)o(e)q(st)o(s.)28
  1481. b(Th)n(us,)17 b(for)f(monk)o(ey)g(t)o(e)q(st)o(s,)i(k)o(eystrok)o(e)q
  1482. (s)g(d)o(et)o(ermin)o(e)q(d)f(b)o(y)g(t)n(h)o(e)g(leadin)o(g)f(bit)o(s)
  1483. 0 1946 y(of)h(t)n(h)o(e)i(ran)o(dom)d(n)n(u)o(m)n(b)q(er)h(m)n(ust)h(b)
  1484. q(e)f(sa)o(t)o(i)q(sf)q(act)o(or)q(ily)f(ran)o(dom)g(an)o(d)i(in)o(d)o
  1485. (ep)q(en)o(d)o(en)o(t.)31 b(Su)o(c)o(h)18 b(RNG's)f(will)f(b)q(e)0
  1486. 1996 y(sa)o(t)o(i)q(sf)q(act)o(ory)d(for)h(most)f(purp)q(os)q(e)q(s.)62
  1487. 2046 y(Th)o(ere)20 b(are)e(an)g(increas)q(in)o(g)h(n)n(u)o(m)n(b)q(er)f
  1488. (of)g(ap)o(plica)o(t)o(ions,)f(h)o(o)o(w)o(ev)o(er,)i(wh)o(ere)g(ad)o
  1489. (equa)o(t)o(e)g(ran)o(domn)o(e)q(ss)f(in)0 2096 y(t)n(h)o(e)d(most)f(s)
  1490. q(igni14can)o(t)f(bit)o(s)i(of)f(a)g(ran)o(dom)e(in)o(t)o(eger)j(or)f
  1491. (u)o(niform)f(v)n(ar)q(ia)o(t)o(e)g(on)h([0,1))f(i)q(s)h(not)h
  1492. (enough.)k(Mon)o(t)o(e)0 2145 y(Carlo)f(s)q(im)n(ula)o(t)o(ions)e(us)q
  1493. (in)o(g)j(sample)q(s)e(of)i(s)q(ev)o(eral)g(millio)o(ns)e(are)i
  1494. (example)q(s,)f(an)o(d)h(anot)n(h)o(er)g(i)q(s)g(us)q(e)g(of)f(t)n(h)o
  1495. (e)0 2195 y(trailin)o(g)13 b(b)o(yt)o(e)g(of)g(a)h(ran)o(dom)e(in)o(t)o
  1496. (eger)i(t)o(o)g(pro)o(vid)o(e)f(t)n(h)o(e)i(domin)o(an)o(t)c(st)o(ep)k
  1497. (in)e(gen)o(era)o(t)o(in)o(g)h(a)f(di)q(scret)o(e)i(ran)o(dom)0
  1498. 2245 y(v)n(ar)q(ia)o(ble.)h((Proba)o(bly)c(t)n(h)o(e)i(f)q(ast)o(e)q
  1499. (st)g(m)o(et)n(h)o(o)q(d)e(for)h(gen)o(era)o(t)o(in)o(g)g(a)g(di)q
  1500. (scret)o(e)h(v)n(ar)q(ia)o(t)o(e)e(i)q(s)h(t)o(o)g(expre)q(ss)j(eac)o
  1501. (h)e(of)e(it)o(s)0 2295 y(proba)o(bilit)o(ie)q(s)f(as)i(a)f(su)o(m)g
  1502. Fg(p)425 2301 y Fd(i)451 2295 y Fl(=)f Fg(k)516 2301
  1503. y Fd(i)530 2295 y Fg(=)p Fl(256)c(+)g Fg(r)679 2301 y
  1504. Fd(i)691 2295 y Fl(.)17 b(Th)o(en)c(t)n(h)o(e)g(require)q(d)h(v)n(ar)q
  1505. (ia)o(t)o(e)e(i)q(s)g(gen)o(era)o(t)o(e)q(d)h(most)f(of)g(t)n(h)o(e)i
  1506. (t)o(im)o(e)0 2345 y(b)o(y)g(fet)o(c)o(hin)o(g)g(a)g(v)n(alue)g(f)q
  1507. (rom)e(a)i(t)o(a)o(ble)g(wit)n(h)g(in)o(d)o(ex)g(a)g(ran)o(dom)f(b)o
  1508. (yt)o(e)h(d)o(et)o(ermin)o(e)q(d)h(b)o(y)f(t)n(h)o(e)h(trailin)o(g)e(8)
  1509. h(bit)o(s)h(of)0 2394 y(a)f(ran)o(dom)e(32-bit)h(in)o(t)o(eger.))62
  1510. 2444 y(So,)19 b(a)e(really)h(go)q(o)q(d)f(ran)o(dom)g(n)n(u)o(m)n(b)q
  1511. (er)g(gen)o(era)o(t)o(or)i(m)n(ust)f(pass)h(monk)o(ey)d(t)o(e)q(st)o(s)
  1512. k(wit)n(h)e(k)o(eystrok)o(e)q(s)h(d)o(e-)0 2494 y(t)o(ermin)o(e)q(d)e
  1513. (b)o(y)g(all)f(p)q(oss)q(ible)i(su)n(bstr)q(in)o(gs)h(of)e(bit)o(s)h
  1514. (of)f(it)o(s)g(ran)o(dom)f(n)n(u)o(m)n(b)q(ers.)29 b(Most,)19
  1515. b(bu)o(t)f(not)f(all,)f(of)h(t)n(h)o(e)0 2544 y(st)o(an)o(d)o(ard)12
  1516. b(RNG's)f(h)o(a)o(v)o(e)g(sa)o(t)o(i)q(sf)q(act)o(ory)g(leadin)o(g)h
  1517. (bit)o(s,)g(bu)o(t)g(it)g(i)q(s)f(quit)o(e)g(di16cul)o(t)g(t)o(o)h(f)
  1518. q(ashion)f(gen)o(era)o(t)o(ors)i(wit)n(h)0 2594 y(sa)o(t)o(i)q(sf)q
  1519. (act)o(ory)g(trailin)o(g)g(bit)o(s.)62 2643 y(Th)n(us,)g(for)f
  1520. (example,)f(a)h(really)g(go)q(o)q(d)g(RNG)f(m)n(ust)h(pass)h(OPSO)h
  1521. (wit)n(h)e(k)o(eystrok)o(e)q(s)i(d)o(et)o(ermin)o(e)q(d)e(b)o(y)g(bit)o
  1522. (s)0 2693 y(1-10,)f(2-11,...,23-3)o(2.)k(Similarl)o(y)m(,)9
  1523. b(it)j(m)n(ust)g(pass)i(OQSO)f(wit)n(h)g(bit)o(s)g(1-5,2-6,...)o(,28)o
  1524. (-32)c(an)o(d)j(DNA)h(wit)n(h)f(bit)o(s)0 2743 y(1-2,2-3,...)o(,31)o
  1525. (-32.)62 2793 y(A)k(few)g(gen)o(era)o(t)o(ors)i(are)e(t)n(h)o(a)o(t)g
  1526. (go)q(o)q(d,)g(ot)n(h)o(ers)h(are)f(not.)24 b(Here)17
  1527. b(i)q(s)f(a)f(su)o(mm)o(ary)f(of)h(kin)o(ds)h(of)f(gen)o(era)o(t)o(ors)
  1528. 0 2843 y(an)o(d)h(t)n(h)o(e)h(ext)o(en)o(t)g(t)o(o)g(whic)o(h)f(t)n(h)o
  1529. (ey)h(pass)h(monk)o(ey)d(t)o(e)q(st)o(s.)27 b(More)17
  1530. b(d)o(et)o(aile)q(d)g(d)o(e)q(scr)q(ipt)o(ions)g(of)f(t)n(h)o(e)h
  1531. (class)q(e)q(s)i(of)845 2978 y(7)p eop
  1532. %%Page: 8 8
  1533. 8 7 bop 0 45 a Fl(gen)o(era)o(t)o(ors)16 b(are)e(in)f([4,)g(5,)g(6,)g
  1534. (7])0 182 y Fi(12)88 b(Su)o(mm)n(ary)21 b(for)h(v)l(ar)q(ious)f(clas)q
  1535. (s)q(e)r(s)h(of)g(RNG's)0 282 y Fa(12.1)56 b(Con)o(gruen)n(t)n(ial)19
  1536. b(Gen)n(era)o(t)o(ors)0 358 y Fl(Th)o(e)q(s)q(e)d(pro)q(d)o(u)o(ce)g(s)
  1537. q(equence)q(s)i Fg(x)495 364 y Fd(n)530 358 y Fl(=)c
  1538. Fg(ax)622 364 y Fd(n)p Fe(00)p Fh(1)697 358 y Fl(+)c
  1539. Fg(b)h Fl(mo)q(d)g Fg(m)p Fl(.)21 b(Th)o(e)16 b(mo)q(d)o(ulus)d
  1540. Fg(m)j Fl(i)q(s)e(b)q(e)q(st)i(t)o(ak)o(en)f(t)o(o)g(b)q(e)g(2)1610
  1541. 343 y Fh(32)1660 358 y Fl(for)0 408 y(sp)q(ee)q(d)j(an)o(d)e(con)o(v)o
  1542. (enience)i(in)e(mo)q(d)o(er)q(n)g(CPU's,)h(bu)o(t)g(a)f(pr)q(im)o(e)f
  1543. (mo)q(d)o(ulus)g(pro)q(d)o(u)o(ce)q(s)j(b)q(et)n(t)o(er)g(trailin)o(g)e
  1544. (bit)o(s.)0 458 y(Th)o(os)q(e)f(wit)n(h)f(pr)q(im)o(e)f(mo)q(d)o(ulus)f
  1545. (s)q(eem)i(t)o(o)g(do)g(w)o(ell)g(on)g(all)f(su)n(bstr)q(in)o(gs)j(of)d
  1546. (bit)o(s)i(for)f(t)n(h)o(e)h(OPSO,)f(OQSO)h(an)o(d)0
  1547. 508 y(DNA)g(t)o(e)q(st)o(s.)24 b(Th)o(ey)16 b(w)o(ould)e(b)q(e)i(t)n(h)
  1548. o(e)g(con)o(gruen)o(t)o(ial)f(gen)o(era)o(t)o(ors)i(of)e(c)o(h)o(oice)g
  1549. (if)g(t)n(h)o(ey)g(w)o(ere)i(not)e(so)g(awkw)o(ard)0
  1550. 557 y(t)o(o)f(implem)n(en)o(t.)62 607 y(Con)o(gruen)o(t)o(ial)i(gen)o
  1551. (era)o(t)o(ors)i(wit)n(h)e(mo)q(d)o(ulus)f(a)h(p)q(o)o(w)o(er)h(of)f(2)
  1552. g(usually)f(do)h(w)o(ell)g(if)f(str)q(in)o(gs)i(of)f(bit)o(s)h(f)q(rom)
  1553. 0 657 y(t)n(h)o(e)f(14rst)h(10)e(or)g(12)g(are)h(us)q(e)q(d)g(t)o(o)g
  1554. (d)o(et)o(ermin)o(e)g(a)f(k)o(eystrok)o(e.)24 b(Bu)o(t)16
  1555. b(not)o(e,)g(f)q(rom)d(a)o(b)q(o)o(v)o(e,)i(t)n(h)o(a)o(t)h(t)n(h)o(e)g
  1556. (Ber)o(k)o(eley)0 707 y(con)o(gruen)o(t)o(ial)c(RNG)f(f)q(aile)q(d)g
  1557. (OPSO)i(wit)n(h)f(k)o(eystrok)o(e)q(s)i(d)o(et)o(ermin)o(e)q(d)e(b)o(y)
  1558. g(t)n(h)o(e)h(leadin)o(g)f(t)o(en)h(bit)o(s.)18 b(Th)o(e)12
  1559. b(wid)o(ely)0 757 y(us)q(e)q(d)g(gen)o(era)o(t)o(or)h
  1560. Fg(x)298 763 y Fd(n)332 757 y Fl(=)e(69069)p Fg(x)504
  1561. 763 y Fd(n)p Fe(00)p Fh(1)579 757 y Fl(mo)q(d)g(2)692
  1562. 742 y Fh(32)738 757 y Fl((t)n(h)o(e)h(syst)o(em)f(gen)o(era)o(t)o(or)h
  1563. (for)f(V)m(ax's))g(s)q(eems)g(t)o(o)h(pass)g(all)e(t)o(e)q(st)o(s)0
  1564. 807 y(d)o(et)o(ermin)o(e)q(d)17 b(b)o(y)g(leadin)o(g)g(bit)o(s,)g(bu)o
  1565. (t)h(it)e(f)q(ails)f(badly)i(on)f(OPSO,)h(OQSO)h(an)o(d)f(DNA)f(if)g
  1566. (bit)o(s)i(b)q(ey)o(on)o(d)e(t)n(h)o(e)0 856 y(14rst)f(13)e(are)i(us)
  1567. q(e)q(d.)0 973 y Fa(12.2)56 b(Shift)18 b(Regi)q(st)n(er)g(Gen)n(era)o
  1568. (t)o(ors)0 1049 y Fl(Pract)o(ical)d(v)o(ers)q(ions)g(of)f(t)n(h)o(e)q
  1569. (s)q(e)i(gen)o(era)o(t)o(ors)h(are)e(p)q(erh)o(aps)h(b)q(e)q(st)f(d)o
  1570. (e)q(scr)q(ib)q(e)q(d)i(b)o(y)d(viewin)o(g)h(a)f(compu)o(t)o(er)h(w)o
  1571. (ord)0 1099 y(as)i(a)h(bin)o(ary)f(v)o(ect)o(or)h Fg(14)r
  1572. Fl(.)29 b(Th)o(en)18 b(t)n(h)o(e)g(s)q(equence)i(i)q(s)c
  1573. Fg(14)r(;)7 b(14)r(T)s(;)g(14)r(T)994 1084 y Fh(2)1015
  1574. 1099 y Fg(;)g(:)g(:)g(:)n Fl(,)17 b(wit)n(h)h Fg(T)23
  1575. b Fl(a)17 b(bin)o(ary)g(m)o(a)o(tr)q(ix.)27 b(Su)o(c)o(h)17
  1576. b(a)0 1149 y Fg(T)j Fl(i)q(s)14 b(c)o(h)o(os)q(en)i(t)o(o)e(m)o(ak)o(e)
  1577. f(t)n(h)o(e)i(p)q(er)q(io)q(d)f(lon)o(g)g(an)o(d)g(implem)n(en)o(t)o(a)
  1578. o(t)o(i)o(on)d(reason)o(a)o(ble;)k(amon)o(g)d(t)n(h)o(e)j(most)f
  1579. (common)0 1199 y Fg(T)6 b Fl('s)17 b(are)h(t)n(h)o(os)q(e)g(of)f(t)n(h)
  1580. o(e)h(example)q(s)e(a)o(b)q(o)o(v)o(e:)24 b Fg(T)f Fl(=)18
  1581. b(()p Fg(I)d Fl(+)c Fg(R)924 1184 y Fh(15)959 1199 y
  1582. Fl()()p Fg(I)16 b Fl(+)11 b Fg(L)1096 1184 y Fh(17)1132
  1583. 1199 y Fl())17 b(for)g(32-bit)f(bin)o(ary)h(v)o(ect)o(ors,)i(an)o(d)0
  1584. 1248 y Fg(T)f Fl(=)11 b(()p Fg(I)h Fl(+)c Fg(R)203 1233
  1585. y Fh(28)238 1248 y Fl()()p Fg(I)k Fl(+)c Fg(L)368 1233
  1586. y Fh(3)387 1248 y Fl())13 b(or)h Fg(T)j Fl(=)12 b(()p
  1587. Fg(I)g Fl(+)c Fg(L)666 1233 y Fh(18)701 1248 y Fl()()p
  1588. Fg(I)k Fl(+)c Fg(R)835 1233 y Fh(13)870 1248 y Fl())14
  1589. b(for)f(31-bit)f(v)o(ect)o(ors.)19 b Fg(R)13 b Fl(an)o(d)g
  1590. Fg(L)h Fl(are)f(m)o(a)o(tr)q(ice)q(s)g(t)n(h)o(a)o(t)0
  1591. 1298 y(e13ect)j(a)f(r)q(igh)o(t)f((left))h(shift)f(of)h(on)o(e)f(p)
  1592. q(os)q(it)o(ion)h(in)f(t)n(h)o(e)h(bin)o(ary)g(v)o(ect)o(or,)g(an)o(d)g
  1593. (addit)o(ion)e(of)i(bin)o(ary)f(v)o(ect)o(ors)j(i)q(s)0
  1594. 1348 y(t)n(h)o(e)e(exclus)q(iv)o(e-or)g(o)o(p)q(era)o(t)o(ion.)20
  1595. b(Shift)14 b(regi)q(st)o(er)i(gen)o(era)o(t)o(ors)g(do)f(p)q(o)q(orly)f
  1596. (on)h(most)f(monk)o(ey)f(t)o(e)q(st)o(s,)k(wit)n(h)d(t)n(h)o(e)0
  1597. 1398 y(except)o(ion)h(of)e Fg(T)k Fl(=)12 b(()p Fg(I)h
  1598. Fl(+)d Fg(L)434 1383 y Fh(18)469 1398 y Fl()()p Fg(I)j
  1599. Fl(+)d Fg(R)606 1383 y Fh(13)641 1398 y Fl())k(or)f(it)o(s)i(transp)q
  1600. (os)q(e,)g(whic)o(h)e(do)h(w)o(ell)f(on)h(most,)f(bu)o(t)h(not)g(all|s)
  1601. q(ee,)0 1448 y(for)g(example,)d(it)o(s)k(p)q(o)q(or)f(p)q(erform)o
  1602. (ance)f(on)h(OPSO)g(a)o(t)g(t)n(h)o(e)h(en)o(d)f(of)f(Sect)o(ion)h(4.)0
  1603. 1564 y Fa(12.3)56 b(Lagge)r(d)18 b(Fib)r(on)o(acci)f(Gen)n(era)o(t)o
  1604. (ors)0 1641 y Fl(Th)o(e)q(s)q(e)d(gen)o(era)o(t)o(ors)g(us)q(e)g(an)e
  1605. (init)o(ial)f(s)q(et)i(of)f(elem)o(en)o(t)o(s)h Fg(x)864
  1606. 1647 y Fh(1)882 1641 y Fg(;)7 b(x)925 1647 y Fh(2)943
  1607. 1641 y Fg(;)g(:)g(:)g(:)e(;)i(x)1060 1647 y Fd(r)1090
  1608. 1641 y Fl(an)o(d)12 b(t)o(w)o(o)h(\lags")e Fg(r)j Fl(an)o(d)e
  1609. Fg(s)h Fl(wit)n(h)g Fg(r)f(>)g(s)p Fl(.)0 1690 y(Su)o(cce)q(ss)q(iv)o
  1610. (e)18 b(elem)o(en)o(t)o(s)e(are)h(gen)o(era)o(t)o(e)q(d)h(b)o(y)e(t)n
  1611. (h)o(e)h(recurs)q(ion,)g(for)f Fg(n)f(>)h(r)q Fl(:)22
  1612. b Fg(x)1190 1696 y Fd(n)1228 1690 y Fl(=)16 b Fg(x)1300
  1613. 1696 y Fd(n)p Fe(00)p Fd(r)1375 1690 y Ff(05)11 b
  1614. Fg(x)1431 1696 y Fd(n)p Fe(00)p Fd(s)1495 1690 y Fl(,)16
  1615. b(wh)o(ere)i Ff(05)e Fl(i)q(s)0 1740 y(som)o(e)10 b(bin)o(ary)h(o)o
  1616. (p)q(era)o(t)o(ion.)16 b(Th)o(e)c(init)o(ial)d((s)q(ee)q(d))k(elem)o
  1617. (en)o(t)o(s)e(are)g(compu)o(t)o(er)h(w)o(ords)f(an)o(d)g(t)n(h)o(e)h
  1618. (bin)o(ary)f(o)o(p)q(era)o(t)o(ion)0 1790 y(migh)o(t)g(b)q(e)i(+,)p
  1619. Ff(00)p Fl(,)p Ff(03)g Fl(or)g Ff(10)g Fl((exclus)q(iv)o
  1620. (e-or).)18 b(F)m(or)13 b(+)g(or)g Ff(00)p Fl(,)g(t)n(h)o(e)h
  1621. Fg(x)p Fl('s)f(migh)o(t)d(b)q(e)k(in)o(t)o(egers)f(mo)q(d)f(2)1461
  1622. 1775 y Fd(k)1494 1790 y Fl(or)h(s)q(in)o(gle-)g(or)0
  1623. 1840 y(dou)n(ble-preci)q(s)q(ion)d(reals)h(mo)q(d)f(1.)16
  1624. b(F)m(or)11 b Ff(03)p Fl(,)f(o)q(dd)h(in)o(t)o(egers)h(mo)q(d)d(2)992
  1625. 1825 y Fd(k)1012 1840 y Fl(.)17 b(W)m(e)10 b(d)o(e)q(s)q(ign)o(a)o(t)o
  1626. (e)h(su)o(c)o(h)h(a)e(gen)o(era)o(t)o(or)i(lo)q(os)q(ely)0
  1627. 1890 y(as)f(F(r,s,)p Ff(05)p Fl(),)g(al)o(t)n(h)o(ough)g(eac)o(h)h
  1628. (lagge)q(d-Fib)q(on)o(acci)e(gen)o(era)o(t)o(or)i(d)o(ep)q(en)o(ds)g
  1629. (on)f(d)o(et)o(ails)g(of)f(t)n(h)o(e)i(part)o(icular)e(bin)o(ary)0
  1630. 1939 y(o)o(p)q(era)o(t)o(ion)j(an)o(d)h(t)n(h)o(e)g(14nit)o(e)g(s)q
  1631. (et)h(of)e(elem)o(en)o(t)o(s)h(it)f(o)o(p)q(era)o(t)o(e)q(s)i(on.)62
  1632. 1989 y(Gen)o(era)o(t)o(ors)i(us)q(in)o(g)e(m)n(ul)o(t)o(iplica)o(t)o
  1633. (ion)d(on)j(o)q(dd)g(in)o(t)o(egers,)h(a)n(u)o(t)o(om)o(a)o(t)o(ically)
  1634. d(mo)q(d)o(ulo)g(2)1382 1974 y Fh(32)1417 1989 y Fl(,)j(are)f(t)n(h)o
  1635. (e)h(b)q(e)q(st)h(of)0 2039 y(t)n(h)o(e)g(lagge)q(d)e(Fib)q(on)o(acci)h
  1636. (gen)o(era)o(t)o(ors,)i(pass)q(in)o(g)f(ot)n(h)o(er)g(t)o(e)q(st)o(s)h
  1637. (as)e(w)o(ell)g(as)g(monk)o(ey)e(t)o(e)q(st)o(s.)27 b((Th)o(e)17
  1638. b(last)f(bit)g(i)q(s)0 2089 y(alw)o(ays)g(1,)h(so)g(of)f(cours)q(e)i(t)
  1639. n(h)o(ey)f(cannot)g(pass)h(OPSO,)f(OQSO)h(or)f(DNA)f(if)g(t)n(h)o(e)i
  1640. (last)e(bit)h(con)o(tr)q(ibu)o(t)o(e)q(s)h(t)o(o)0 2139
  1641. y(t)n(h)o(e)c(k)o(eystrok)o(e.))19 b(Ov)o(erall,)13
  1642. b(F(r,s,+))h(an)o(d)f(F(r,s,-))h(an)o(d)f(F(r,s,)p
  1643. Ff(10)p Fl())h(do)f(v)o(ery)h(w)o(ell)f(on)g(monk)o(ey)f(t)o(e)q(st)
  1644. o(s)k(for)d(all)0 2188 y(str)q(in)o(gs)j(of)f(bit)o(s.)24
  1645. b(Bu)o(t)17 b(F(r,s,)p Ff(10)p Fl())f(m)o(ay)e(f)q(ail)f(for)j
  1646. (pairs)f((r,s))h(su)o(c)o(h)h(as)e((31,13))g(or)h((17,5))e(b)q
  1647. (eca)n(us)q(e)j(of)e(t)n(h)o(e)q(ir)0 2238 y(t)n(h)o(e)q(ir)i(in)o(ad)o
  1648. (equa)o(t)o(e)g(p)q(er)q(io)q(d,)g(2)476 2223 y Fd(r)494
  1649. 2238 y Fl(,)g(in)f(con)o(trast)h(t)o(o)g(t)n(h)o(e)g(ot)n(h)o(er)h
  1650. (lagge)q(d)e(Fib)q(on)o(acci)g(gen)o(era)o(t)o(ors,)j(whic)o(h)d(h)o(a)
  1651. o(v)o(e)0 2288 y(p)q(er)q(io)q(ds)e(a)o(b)q(ou)o(t)g(2)284
  1652. 2273 y Fh(32+)p Fd(r)361 2288 y Fl(.)k(See)c([5].)0 2404
  1653. y Fa(12.4)56 b(A)-6 b(W)n(C)19 b(an)n(d)h(SWB)e(Gen)n(era)o(t)o(ors)0
  1654. 2481 y Fl(Th)o(e)j(recen)o(t)n(ly)g(d)o(ev)o(elo)o(p)q(e)q(d)g(add-wit)
  1655. n(h-carry)g((A)-5 b(W)o(C))21 b(an)o(d)f(su)n(btract-wit)n(h-b)q
  1656. (orro)o(w)h((SWB))g(gen)o(era)o(t)o(ors)0 2531 y([7)o(])16
  1657. b(h)o(a)o(v)o(e)h(rem)o(ar)o(ka)o(bly)d(lon)o(g)i(p)q(er)q(io)q(ds)h
  1658. (an)o(d)f(s)q(eem)g(t)o(o)h(pass)h(OPSO,)e(OQSO)i(an)o(d)e(DNA)h(t)o(e)
  1659. q(st)o(s)h(for)e(str)q(in)o(gs)0 2581 y(of)j(bit)o(s)i(f)q(rom)d(all)h
  1660. (part)o(s)i(of)e(t)n(h)o(e)i(ran)o(dom)d(in)o(t)o(eger.)37
  1661. b(Th)o(ey)21 b(are)f(bas)q(e)q(d)h(on)f(recurs)q(ions)h(su)o(c)o(h)f
  1662. (as)h Fg(x)1634 2587 y Fd(n)1678 2581 y Fl(=)0 2630 y
  1663. Fg(x)24 2636 y Fd(n)p Fe(00)p Fd(r)97 2630 y Fl(+)9
  1664. b Fg(x)162 2636 y Fd(n)p Fe(00)p Fd(s)235 2630 y Fl(+)g
  1665. Fg(c)i Fl(mo)q(d)f Fg(b)p Fl(,)j(wh)o(ere)i(t)n(h)o(e)f(`)p
  1666. Fg(c)p Fl(')f(i)q(s)g(not)g(a)g(const)o(an)o(t,)h(bu)o(t)g(t)n(h)o(e)h
  1667. (carry)f(bit:)j(1)d(or)f(0,)g(d)o(ep)q(en)o(din)o(g)h(on)0
  1668. 2680 y(wh)o(et)n(h)o(er)i(t)n(h)o(e)g(previous)f(addit)o(ion)e(did,)h
  1669. (or)h(did)f(not,)h(excee)q(d)i(t)n(h)o(e)e(mo)q(d)o(ulus)e
  1670. Fg(b)p Fl(.)21 b(Th)o(a)o(t)14 b(d)o(e)q(scr)q(ib)q(e)q(s)i(an)f(A)-5
  1671. b(W)o(C)0 2730 y(gen)o(era)o(t)o(or.)19 b(An)14 b(SWB)g(gen)o(era)o(t)o
  1672. (or)h(forms)d Fg(x)695 2736 y Fd(n)729 2730 y Fl(=)g
  1673. Fg(x)797 2736 y Fd(n)p Fe(00)p Fd(s)870 2730 y Ff(00)d
  1674. Fg(x)935 2736 y Fd(n)p Fe(00)p Fd(r)1009 2730 y Ff(00)g
  1675. Fg(c)j Fl(mo)q(d)e Fg(b)p Fl(,)j(wit)n(h)h Fg(c)f Fl(1)h(or)g(0,)f(d)o
  1676. (ep)q(en)o(din)o(g)h(on)0 2780 y(wh)o(et)n(h)o(er)h(t)n(h)o(e)g
  1677. (previous)f(su)n(btract)o(ion)h(w)o(as)f(n)o(ega)o(t)o(iv)o(e.)845
  1678. 2978 y(8)p eop
  1679. %%Page: 9 9
  1680. 9 8 bop 62 45 a Fl(An)16 b(example:)k(t)n(h)o(e)c(SWB)g(gen)o(era)o(t)o
  1681. (or)h Fg(x)703 51 y Fd(n)740 45 y Fl(=)e Fg(x)811 51
  1682. y Fd(n)p Fe(00)p Fh(24)903 45 y Ff(00)10 b Fg(x)969
  1683. 51 y Fd(n)p Fe(00)p Fh(37)1061 45 y Ff(00)h Fg(c)g
  1684. Fl(mo)q(d)f(2)1245 30 y Fh(32)1296 45 y Fl(h)o(as)16
  1685. b(p)q(er)q(io)q(d)f(a)o(b)q(ou)o(t)h(2)1642 30 y Fh(1178)0
  1686. 95 y Fl(an)o(d)d(pass)q(e)q(s)j(all)c(t)n(h)o(e)j(CA)m(T,)e(OPSO,)h
  1687. (OQSO)h(an)o(d)e(DNA)h(t)o(e)q(st)o(s)i(pu)o(t)e(t)o(o)g(it,)f(for)g
  1688. (all)g(su)n(bstr)q(in)o(gs)j(of)d(it)o(s)h(32-bit)0 145
  1689. y(in)o(t)o(egers.)27 b((Ho)o(w)o(ev)o(er,)18 b(it)e(i)q(s)g(not)g(p)q
  1690. (erfect;)j(it)d(f)q(ails)f(t)n(h)o(e)j(birt)n(h)o(d)o(ay-spacin)o(g)f
  1691. (t)o(e)q(st)h(d)o(e)q(scr)q(ib)q(e)q(d)g(in)e([4)o(],)g(as)h(do)0
  1692. 195 y(ot)n(h)o(er)e(A)-5 b(W)o(C)14 b(an)o(d)f(SWB)h(gen)o(era)o(t)o
  1693. (ors)i(an)o(d)d(lagge)q(d-Fib)q(on)o(acci)g(gen)o(era)o(t)o(ors)j(us)q
  1694. (in)o(g)e(+,{)f(or)h Ff(10)p Fl(.))0 311 y Fa(12.5)56
  1695. b(MW)n(C)19 b(gen)n(era)o(t)o(ors)0 387 y Fl(Th)o(e)13
  1696. b(most)e(sa)o(t)o(i)q(sf)q(act)o(ory)h(of)g(all)f(gen)o(era)o(t)o(ors)j
  1697. (I)e(h)o(a)o(v)o(e)g(cons)q(id)o(ere)q(d)i(in)e(t)n(h)o(e)h(past)g(35)f
  1698. (y)o(ears)h(are)g(m)n(ul)o(t)o(iply-wit)n(h-)0 437 y(carry)i(gen)o(era)
  1699. o(t)o(ors,)i(d)o(e)q(scr)q(ib)q(e)q(d)f(in)f(a)f(p)q(ost)o(scr)q(ipt)j
  1700. (14le)e((m)o(wc1.ps))f(includ)o(e)q(d)h(in)g(t)n(h)o(e)g(DIEHARD)g
  1701. (pac)o(kage.)0 487 y(Th)o(ey)j(pass)h(all)e(t)o(e)q(st)o(s)j(pu)o(t)f
  1702. (t)o(o)f(t)n(h)o(em,)g(h)o(a)o(v)o(e)g(v)o(ery)h(lon)o(g)e(p)q(er)q(io)
  1703. q(ds)h(an)o(d)g(are)g(part)o(icularly)f(w)o(ell)h(suit)o(e)q(d)g(for)0
  1704. 537 y(compu)o(t)o(er)c(implem)n(en)o(t)o(a)o(t)o(io)o(n.)0
  1705. 653 y Fa(12.6)56 b(Com)m(bin)o(a)o(t)n(ion)17 b(Gen)n(era)o(t)o(ors)0
  1706. 730 y Fl(Th)o(ere)j(i)q(s)f(t)n(h)o(eoret)o(ical)g(an)o(d)g(empir)q
  1707. (ical)d(sup)o(p)q(ort)k(for)f(t)n(h)o(e)g(id)o(ea)h(t)n(h)o(a)o(t)f
  1708. (com)n(binin)o(g)e(t)o(w)o(o)i(ran)o(dom)e(n)n(u)o(m)n(b)q(er)0
  1709. 779 y(gen)o(era)o(t)o(ors)f(pro)q(d)o(u)o(ce)q(s)g(a)e(gen)o(era)o(t)o
  1710. (or)h(wit)n(h)g(b)q(et)n(t)o(er)g(ran)o(domn)o(e)q(ss)g(t)n(h)o(an)f(e)
  1711. q(it)n(h)o(er)i(of)d(it)o(s)i(comp)q(on)o(en)o(t)o(s)f([4].)k(F)m(or)0
  1712. 829 y(example,)10 b(cons)q(id)o(er)j(t)n(h)o(e)f(s)q(imple)e(con)o
  1713. (gruen)o(t)o(ial)h(gen)o(era)o(t)o(or)j Fg(x)963 835
  1714. y Fd(n)996 829 y Fl(=)e(69069)p Fg(x)1169 835 y Fd(n)p
  1715. Fe(00)p Fh(1)1244 829 y Fl(mo)q(d)e(2)1356 814 y Fh(32)1403
  1716. 829 y Fl(ap)o(plie)q(d)h(t)o(o)h(OPSO)0 879 y(for)i(bit)o(s)h(15-24,)e
  1717. (OQSO)j(for)e(bit)o(s)h(15-18)e(an)o(d)i(DNA)f(for)g(bit)o(s)h(15-16.)k
  1718. (It)c(f)q(ails)e(all)g(of)h(t)n(h)o(em)g(sp)q(ect)o(acularly)m(,)0
  1719. 929 y(pro)q(d)o(u)o(cin)o(g,)c(re)q(sp)q(ect)o(iv)o(ely)m(,)h(984,860)d
  1720. (an)o(d)i(983,840)e(an)o(d)h(983,840)f(mi)q(ss)q(in)o(g)g(w)o(ords)j
  1721. (wh)o(en)f(141,909)e(are)i(exp)q(ec-)0 979 y(t)o(e)q(d.)18
  1722. b(Bu)o(t)13 b(if)d(w)o(e)i(com)n(bin)o(e)f(it)g((b)o(y)h(addit)o
  1723. (ion))e(wit)n(h)i(t)n(h)o(e)g(shift)g(regi)q(st)o(er)g(gen)o(era)o(t)o
  1724. (or)h Fg(14)h Fl(=)e Fg(14)r Fl(()p Fg(I)d Fl(+)c
  1725. Fg(L)1495 964 y Fh(17)1531 979 y Fl()()p Fg(I)k Fl(+)c
  1726. Fg(R)1659 964 y Fh(15)1694 979 y Fl())0 1029 y(on)12
  1727. b(32)g(bit)o(s)g((whic)o(h)g(f)q(ails)f(sp)q(ect)o(acularly)h(on)g
  1728. (all)f(su)n(bstr)q(in)o(gs)j(of)e(bit)o(s),)h(w)o(e)f(get)h(t)n(h)o(e)
  1729. q(s)q(e)g(mi)q(ss)q(in)o(g-w)o(ord)e(cou)o(n)o(t)o(s)0
  1730. 1078 y(for)j(OPSO,bit)o(s)h(15-24:)i(141909;)12 b(OQSO,)i(bit)o(s)h
  1731. (15-18:)i(142116;)12 b(an)o(d)i(DNA,)f(bit)o(s)i(15-16:)i(141,524.)g(V)
  1732. m(ery)0 1128 y(go)q(o)q(d,)c(b)q(e)q(in)o(g)h(0,.762)e(an)o(d)h(-.092)g
  1733. (st)o(an)o(d)o(ard)h(d)o(evia)o(t)o(ions)g(f)q(rom)e(t)n(h)o(e)i(m)o
  1734. (ean.)62 1178 y(Thi)q(s)k(example)e(i)q(s)i(for)g(t)n(h)o(e)g(wid)o
  1735. (ely)g(us)q(e)q(d)h(com)n(bin)o(a)o(t)o(ion)d(gen)o(era)o(t)o(or)j(Sup)
  1736. q(er-Dup)q(er,)g(com)n(binin)o(g)e Fg(I)22 b Fl(=)0 1228
  1737. y(69069)11 b Ff(03)h Fg(I)22 b Fl(wit)n(h)c Fg(14)k
  1738. Fl(=)d Fg(14)r Fl(()p Fg(I)e Fl(+)12 b Fg(L)530 1213
  1739. y Fh(17)566 1228 y Fl()()p Fg(I)k Fl(+)c Fg(R)708 1213
  1740. y Fh(15)743 1228 y Fl().)32 b(Bu)o(t)19 b(ev)o(en)g(t)n(h)o(a)o(t)g
  1741. (com)n(bin)o(a)o(t)o(ion)c(f)q(ails)i(monk)o(ey)g(t)o(e)q(st)o(s)j(on)0
  1742. 1278 y(trailin)o(g)f(bit)o(s.)38 b(Th)o(e)20 b(KISS)h(gen)o(era)o(t)o
  1743. (or)g((K)o(eep-It-Simple-St)o(upid))e(i)q(s)h(an)g(example)e(of)i(a)g
  1744. (com)n(bin)o(a)o(t)o(ion)0 1327 y(gen)o(era)o(t)o(or)f(t)n(h)o(a)o(t)f
  1745. (i)q(s)f(a)o(b)q(ou)o(t)h(as)g(s)q(imple)d(as)j(on)o(e)g(can)g(b)q(e)g
  1746. (an)o(d)f(h)o(a)o(v)o(e)g(v)o(ery)i(lon)o(g)e(p)q(er)q(io)q(d,)h(a)o(b)
  1747. q(ou)o(t)g(2)1563 1312 y Fh(127)1614 1327 y Fl(,)g(an)o(d)0
  1748. 1377 y(pass)d(all)e(t)o(e)q(st)o(s)i(on)f(all)f(str)q(in)o(gs)h(of)g
  1749. (bit)o(s.)k(It)c(com)n(bin)o(e)q(s)f(a)h(con)o(gruen)o(t)o(ial,)f(a)h
  1750. (tr)q(iple-shift)e(regi)q(st)o(er)j(gen)o(era)o(t)o(or,)0
  1751. 1427 y(an)o(d)g(a)g(m)n(ul)o(t)o(iply-wit)n(h-carry)e(gen)o(era)o(t)o
  1752. (or:)23 b Fg(I)18 b Fl(=)c(69069)9 b Ff(03)h Fg(I)d
  1753. Fl(+)s(1,)16 b Fg(14)h Fl(=)d Fg(14)r Fl(()p Fg(I)h
  1754. Fl(+)10 b Fg(L)1250 1412 y Fh(13)1286 1427 y Fl()()p
  1755. Fg(I)k Fl(+)c Fg(R)1424 1412 y Fh(17)1459 1427 y Fl()()p
  1756. Fg(I)k Fl(+)d Fg(L)1594 1412 y Fh(5)1613 1427 y Fl())k(an)o(d)0
  1757. 1477 y Fg(z)19 1483 y Fd(n)53 1477 y Fl(=)d(2)p Fg(z)137
  1758. 1483 y Fd(n)p Fe(00)p Fh(1)212 1477 y Fl(+)d Fg(z)272
  1759. 1483 y Fd(n)p Fe(00)p Fh(2)347 1477 y Fl(+)g(carry)j(mo)q(d)f(2)606
  1760. 1462 y Fh(32)640 1477 y Fl(.)0 1614 y Fi(Reference)r(s)0
  1761. 1705 y Fl([1])20 b(Gra)o(h)o(am,)26 b(Ron)o(ald)e(L.,)j(Kn)n(u)o(t)n
  1762. (h,)j(Don)o(ald)24 b(E.)i(an)o(d)f(P)o(a)o(t)o(ashnik,)i(Oren)g
  1763. Fk(Concr)n(ete)e(Mathematics)p Fl(,)65 1755 y(Addi)q(son-W)m(e)q(sley)m
  1764. (,)12 b(Readin)o(g,)h(MA)h(1989)0 1838 y([2])20 b(Haas,)h(Alexan)o(d)o
  1765. (er,)h(Th)o(e)e(m)n(ul)o(t)o(iple)e(pr)q(im)o(e)g(ran)o(dom)h(n)n(u)o
  1766. (m)n(b)q(er)h(gen)o(era)o(t)o(or,)i Fk(A)o(CM)e(T)m(r)n(ansactions)g
  1767. (on)65 1888 y(Mathematic)n(al)14 b(Softwar)n(e)p Fl(,)f
  1768. Fj(13)p Fl(,)g(No.)h(4,)f(1987.)0 1971 y([3])20 b(Marsaglia,)26
  1769. b(George,)i(Ran)o(dom)23 b(n)n(u)o(m)n(b)q(ers)i(f)q(all)e(m)o(ainly)g
  1770. (in)i(t)n(h)o(e)h(plan)o(e)q(s,)h Fk(Pr)n(o)n(c)n(e)n(e)n(dings)e
  1771. (National)65 2021 y(A)n(c)n(ademy)15 b(Scienc)n(e)g Fj(61,)h
  1772. Fl(25-28,)c(1968.)0 2104 y([4])20 b(Marsaglia,)f(George,)i(K)o(eynot)o
  1773. (e)f(Addre)q(ss:)32 b(A)20 b(Curren)o(t)h(View)e(of)g(Ran)o(dom)f(Nu)o
  1774. (m)n(b)q(er)h(Gen)o(era)o(t)o(ors,)65 2153 y Fk(Pr)n(o)n(c)n(e)n(e)n
  1775. (dings,)c(Computer)h(Scienc)n(e)g(and)h(Statistics:)j(16th)c(Symp)n
  1776. (osium)g(on)g(the)g(Interfac)n(e,)g Fl(Els)q(evier,)65
  1777. 2203 y(1985)0 2286 y([5])k(Marsaglia,)9 b(George)i(an)o(d)g(Tsay)m(,)g
  1778. (L.)f(H.,)g(Ma)o(tr)q(ice)q(s)i(an)o(d)e(t)n(h)o(e)i(stru)o(ct)o(ure)h
  1779. (of)d(ran)o(dom)f(n)n(u)o(m)n(b)q(er)i(s)q(equence)q(s,)65
  1780. 2336 y Fk(Line)n(ar)j(A)o(lgebr)n(a)g(and)i(its)e(Applic)n(ations,)h
  1781. Fj(67,)h Fl(147{156,)11 b(1985.)0 2419 y([6])20 b(Marsaglia,)10
  1782. b(George,)h(Th)o(e)g(m)o(a)o(t)n(h)o(em)o(a)o(t)o(ics)e(of)h(ran)o(dom)
  1783. f(n)n(u)o(m)n(b)q(er)i(gen)o(era)o(t)o(ors,)i Fk(Pr)n(o)n(c)n(e)n(e)n
  1784. (dings)f(of)g(Symp)n(osia)65 2469 y(on)j(Applie)n(d)g(Mathematics,)g
  1785. Fj(46,)g Fl(73{89,)e(1992.)0 2552 y([7])20 b(Marsaglia,)13
  1786. b(George)j(an)o(d)f(Zam)o(an,)e(Ar)q(if,)h(A)i(n)o(ew)f(class)h(of)f
  1787. (ran)o(dom)e(n)n(u)o(m)n(b)q(er)i(gen)o(era)o(t)o(ors,)i
  1788. Fk(A)o(nnals)f(of)65 2602 y(Applie)n(d)e(Pr)n(ob)n(ability,)g
  1789. Fj(1,)i Fl(No.)d(3,)g(462{480,)f(1991.)0 2685 y([8])20
  1790. b(Whit)n(t)n(le)q(s)q(ey)m(,)15 b(J.)g(R.)f(B.,)h(On)h(t)n(h)o(e)g(m)n
  1791. (ul)o(t)o(idim)n(ens)q(ion)o(al)11 b(u)o(niformit)o(y)i(of)i(ps)q
  1792. (eudoran)o(dom)f(n)n(u)o(m)n(b)q(er)h(gen)o(er-)65 2734
  1793. y(a)o(t)o(ors,)f Fk(Communic)n(ations)h(of)g(the)g(A)o(CM,)f
  1794. Fj(12)p Fl(,)f(p.)h(247,)e(1969.)845 2978 y(9)p eop
  1795. %%Trailer
  1796. end
  1797. userdict /end-hook known{end-hook}if
  1798. %%EOF
  1799.