Handbook of Theoretical Computer Science. Volume A: Algorithms and Complexity

975 Pages·1990·10.09 MB·English

by  Jan van Leeuwen (ed.)

Managing Editor
VALNE EUWEN,
J. Utrecht
AdvisBoorayr d
A.MRE.Y ER,
CambrgieMd,A
MN.VI AT,
Paris
M.PSTA.E RSON,
Coventry
PERRIN,
Paris
D.
ELSEVIER THEM ITP RESS
AMSTERD•AN ME WY ORK• OXFOR•TD O KYO CAMBRIDMGAES,S ACHUSETTS
HandboookfT heoretCiocmaplu tSecri ence
Volume A
ALGORITHMSA ND COMPLEXITY
editbeyd
JANV AN LEEUWEN,
UtrecUhnti versTihteNy e,t herlands
1111111
1990 1990
ELSEVIER THEM ITP RESS
AMSTERD•AN MEWY OR•KO XFOR•DT OKYO CAMBRIDMGAES,S ACHUSETTS
ELSEVIESRC IENCPEU BLISHERBS. V.
P.O.B ox2 11,
1000 AE AmsterdaTmhe,N etherlands
Co-publisfhoterhr esU niteSdt atCeasn,a daa,n dJ apan:
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LibraorfCy o ngrCeasst aloging-in-DPuabtlai cation
Handboookf t heoretciocmaplu tsecri ence/eJdainvt aonr ,L eeuwen.
p. cm.
Includbeisbl iograrpehfiecraelan ncdei sn dexes.
Contenvt.As .:A lgoritahnmdcs o mplexivt.yB .F ormamlo dels
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ands emantics.
ISBN0 -444-880(7U5.-S5:. s et-)-I.S BN0 -444-880(7U1.-S2:. v .
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I.
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CIP
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copyriqguhets tiionncsl,u dpihnogt ocopoyuitnsgi odfte h eU .S.As.h,o ubledr efertroet dh peu blisher.
No responsiibsia lsistuym ebdy t heP ublisfhoerar n yi njuarnyd /odra magteo p ersoonrsp roperatsay
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PrintienTd h eN etherlands Printoenda cid-frpeaepe r
Preafce
Modedrenv eloipcnmo emnptausnts deo rf tswyasrtheea mvrsea i msaencdyh alleng­
inigs scuoensc etrhndeie nsagin gednffi cioefnc coym pplreoxg raampmpilnigc a­
tioTnhsei.ras en i ncreasfoir"n agd vnatenhecedeo tdrou y n"d,e rasntedax npdl oit
basic caonmndec cehpatnsii ncs ommsp uatniidnn gfo rmaptroicoenTs hsei ng.
HandobTfo hoekoC roemtpSiucctiaieeldsrne scieg pnreodva wi tidod�e eu dioefn ce
professainosdnt auldisen Cn otmsp uStceirea nncrdee ladtiesdc iwpiltaihnn es
overovfti hemewaj orre saunlddte sv eloipntm hetenh teso reextpilcoaorlfa tion
these diastseu.e s to
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algortihtaahrtnme es e dOentd ho.et heri pthr aonvcdio,dn ecasen pldta sn gtuaog es
capttuhreees seinnac leg,o raintddhe msiccr tieprtmisav,nes y y osftfr eomm
specitfieocffia ctiiieomlnnpet m enBtuattthmi eao tnh.e mfraatmiecwatolhrh akatsv e
provebdei ntvoa lfourCa obmlpeuS tceirea nrucese ei dn creianms ainnoygt lhye r
disciapsl iwWneheleslr .en voetrio ofin nsfo rmoarti inofonr mpartoicoenas rsei ng
identqiufieesdot,fir oenprse saenncdto amtpiuotcnaa btneifo ornm aliincz oemd­
putsecri etnecrTemh se.o rCeotmipcuaStlce irec nocneci etrswneislt afhlfo lr mal
modaenlds meatnahdlot lde sc hnoifdqe usecsra inpadtn iaoltnyh saairtrse e qeudi r
int his domain.
Asa c onseqtuheeanrrmceeae n fayc ettoTs h eorCeotmipcuSatclei reA nsac e.
disciietpm lpilnaoedy vsa tneccehdn frioqmMu aetsh emaantLdio cgsic a,tt hbeu t
samtei mhea si te stablismhoeddae nlifudstn sd aomwenn tfiaownlrh miracelhs ults
thoer iginal hmaovrteei mvaaivtniiesodiTn bhsleH e a.n dobfTo hoeko retical
CompSuctieaetrnt cetmeopo etffrsa ni n-dveipeotwfht hfiee lodfT heoretical
CompuStceirea nsc weah oblyea ,c omprehensiovfte h seec xipeonstiitfiico n
advainntc heaisrs e a.
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thmea tetrtoih raeel c ogcnoiarzreee odaTf sh eorCeotmipcuSatclei re ncwei.t hE ven
thriess triimcptofisruoetndhc ,eh ro ihcatedobs e m adient hseu bjceocvtesr ed and
theex toeftn htme a teprrioavloi nde eadcs huj becTthc.eu rrveenrtso ifto hne
Handbiopsor ke sientn twveood l umes:
VolA.:A logritahnmCdso mplexity
VolB.:F ormal aMnoSdde emlasn tics
This omrJo errsees fl etchdteis v ibseitowanel egno riietnhatmne-dddoe rscription­
oriernetseedta hrcacathbn e w itneisnTs heedo rCeotmipcuatle ra nSidct i ence,
seemneadt utrofoa lll iotw tfhoebrso eo Wkhse.r tehaveso lucmaens u sbeed
ii PREFAEC
indepetnhdeearnrmetea l niyyn, t erceosntnientcghts aihtoo tnwhs a t atrheea st wo
reaalrlheyi gihnltye rTtowgienttehhdvee.or l,u gmieavsu e n iiqmuep reosfs ion
reseiaTnrh ceho rCeotmipcuSatclei rea nsiic tpse r acttoidsIaenfydo fo. tr r eference
purpwoesh eosp,e yuostue h ewbsioelot lkog s e atfe elfoirnt ght eh reeotwiocrakl
thiagsto ionnig nt hmea ny ofifCe olmdpsuS tceireo nrtc ose i mspalytyy i osufr
curiosity.
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modoecflos m putcaotmipoltneh,xe idotarysty ta,r uacnteduffi rceicseo nmtp utation
inm anrye cogsnuibzdeids ocfTi hpeloirnCeeotsmi pcuaStlce ireV nocleuB.m e
presentosf ma at ecorhntio haitelch ee oofar uyt oamnardte aw rsiytsitnteghm es ,
foundaotmfio odnepsrr no gralmamnignulgao ggfoeirpsc r,so gsrpaemc iafincda tion
verificaatn iuomnbo,esf rt a unaddii meaesttd h e thmeoodreeoltafiid ncvgaa ln ced
computing applichaatvieo onbrseg.ea nntB ioroz eteflhtde h cdveteo vleulmoeps­
menotfT heorCeotmipcuaStlce irefr nocmie t csl asrsoiocttaotsl h meo dern
complexeittaiyncl-d ot gahipecpo rrotaofoc,hre e xsa mppalreaa,ln dldie slt ributed
compuItnmi onscgta. s eesx taenbn isbilvieoh gabrsea eppnrh oyv tioad sesdii ns t
fuhrestrt uodtfyh fi ee alndfid n dsipnegcs iocfiuedcr o cumfoerfun rttsrh eeferr ence.
Specaitfitceh natbsie oenn tgoais vternu cdteuvreeldoo pftmh meean tte irnti hael
varicohuaspi tne rostr omd aektreh H ea ndbloaorksg ee-llcfyo ntHaoiewnveedr.,
somfaem iliwairtCihot myp uStceirea ntac nue n derglreavdieauslsa stuem ed.
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identthinefie eefoddra c ompreahneednn sciyvcel opeodnti hfceu ntdraemaetnitsael
areoaTfsh eorCeotmipcuSatclei reT nhacede v.i bsooacrroydn sioAsft. MiRen.yg e r
(CambrMiAd)g,Ne i,Mv (.aaP tr iMs.)S,. P(aCtoevreasnnotDdnr.P y e)r( rPianr is)
waisn struimne ndteatfilhn ei nvegea rrsloiyfto hnHe a ndbporookjT ehcet .
compplreotjee hcats trnheoaswtui ltnth eed pvroelsuhemangestrs o fawrbn e yond
thlei moirtisg ifonreaslefolerynt hHea ndbaonoodkn ,lb ye caoufts hele o yal
suppooafrl ctlo ntrcioblulteitanotgg hpu ere oshj aeiscbtt e epno ssticobo lmep lete
thgei gatnatosifpkcr esetnhcteui rnrogev netro vftih ecewo arree oaTfsh eoretical
ComputerI w Soculiliedtkn otec h ea.an laklu thors, btohaear ndtad hd ev isory
editoraitaE ll sesSvtciaieffePr nu cbel ifosrht ehreisin rv alsuuapbplaoenr dt
contritbotu hHteai nodnbspo rookj ect.
Jv.a Lne euwen
ManaEgdiintgo r
Utre1c9h9t0,
Lisotf C ontributtooV rosl ume
A
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CHAPT1E R
MachinMeo delasn dS imulations
PetvearnE MDEB OAS
DepartomfMe antth emaatniCdco sm puStceire nUcnei,v eorfsA imtsyt erdam.
PlantMaugied erg2r4a1,c0 h1t8 AmsterNdeatmh,e rlaanndd s,
CentforrMe a themTaaVtn iCdco sm puStceire nce,
Kruis4l1a,3a1 n0 9S8J A msterNdeatmh,e rlands
Contents
Introduction 3
2I..S equentmiaaclh inmeo dels 16
3.Th es econmda chincel as.s 38
4.Pa rallmealc hinmeo delosu tsitdhee s econmda chincel ass 54
Acknoweldgment 60
Referenc.e s 61
HANDBOOK OF THEORETICALC OMPUTER SCIENCE
Editebdy vanL eeuwen
© ElsevJSi.ce ire nPcueb lishBe.rVs.1 ,9 90
MACHIMNOED ELASN DS IMULATIONS 3
1.I ntroduction
Thset uodfcy o mputcaotmipolnreaexlqi uttihyra etsa gornoeenea ms o doefl
computnaotrimocanal,lla lym e adc mhoidnfoeree le ff,ct uaaltgionrgUi ntfohrm­s.
tunamtaenlyy dmiaffcehrmieonndethe albvsee pe rn opiotnsh epeda rsatn,g frionmg
theordeetvilicictakehlTese u rmiancgh tiomn oero erl e rsesa lmiosdtoeirflca s n dom
accmeascsh ainnpdea sr aclolmepluC toenrsse.q tuheeanrrtmeela ynn yo tioofn s
computcaotmipolndeaexlpi etnyd,ti hmneag c hominon deoe nlle i tkoaed so apntd,
there bsene oe mu nntioofot riomtof n iosmsr e p caocmep lIetnxh icithsya .pw tewe irl l
expltohmreoe rf neud ameanstpaeolcf t cso mipmnla ecxhmiiotndyeae nladsd dress
thqeu esttowi hoaentx ttehnet machcionmep-lmbeeaxasisetfoudyrr t ehvsea rious
modealrse roerdl ieaffrteeWndet w .ii ldle ynt thuienf yiifnpgr inctihpbaliten sd
machmiondeet losg etsheettrh eaompr a brytc ,r itoefer ffiicai foernmc uyt ual
simulations.
1.T1.hi eni vaaonrcfc oem puctoamtpitlohenexaoilrt yy
Iofn wea nttors e asonc oambpolumetex aistsuyur ceahsst htei maens dp ace
consubmyae nad l gortihtoehnnmme u, ss tpi efpcyr ecwihsanetol tyio otfni asmn ed
spaacreme e aTnhtce.o nventioonfta ilma enns dop tacicooemn psl weixtihtiyn
theorceotmipcusatclei rea nrbceae s oendt he imploefma elngtoarotinit ohnm s
abstmraacchtic naelmsla,ec dm hoidnTeehlse ts uo.df y commpelaesxiuinrrte eyas l
compuitnseo prtus r siunte hde boercya,iu wtso eu ldt hmreae kseu lts dependent on
existteicnhgna onlhdoa gryd pweacruel riaatrthihetaorinni e nss aingmdha tt hema­
tiecxaple rRiaetnhtceherr.,o s uugihtm aabclhmeio ndeeo lnaset tetmopp rtosv ide
ar easonable oawfph paortnmo eix giehmxtap iteafirc oetcna o lm pwuetrueesrfo e rd
onec'osm putations.
Steivlielwfn,eb acsoem pltehxeiootnary by s tracotcf o inncsrteetaetd h mea chines,
arbitroaftr hciehn oeoisfacsm e o dreelm aIiitnas stt . h piosi tnhtta hte nooft ion
simuelnatIetwfrie spo .rn e smeunttus ailm ulbaettiwotenwesmon o dealngsdi ve
estifomrta htteei sam nesd p ace overbhype eardfosr miinncgu rtrhweeeds e simulations,
shoiwfan c tth at tahnsedp atccioemm ep leixntih ttewi oe sm doond oedtlie sffbr y
more tthgheia vone vne frcahteToahrsdesi oz.tfe h oev erfahcetatoder ulsstl wosh at
extaesnste ratbiocouontms p laerxmeia tcnyhe i-baanstdeow d h aetx ttehnaetry e
machine-independent.
Theex isotmfea nndcyiee ffr emnatc hmiondede olnesos nt e cesmseaatrnhit alhtye re
arneou nifournmd ernloytiionofcgn o sm putcaotmipolnIeantxl hi teth ye.oo fr y
computala atrvigaoerno i mfeo tdyae nlfodsr mcaall hcaubsle ie n ptrcooa ppotsuerde
thneo toiefoeff nc tciovmep utTahthiiasnos oln te. ta aodp roliofecfro amtpiuotna tion
theodrutietoe h sbe,a sfaictcth tahtpe r oposed hfoaravmlebal el seihns omtwsbon e
equiviatnlh foeeln lto sweinnesgaec c:oh m putioannt foeir omna claibnses m i mulated
byac omputiatnth oieto hfoner rm alFirsotmmh.e e q uivoanlceeo nnccetl huadtes i f
ap robilusen ms olvoanpbeal ret miiocndu telhlaie,ritn as l usnos olfovraa lobltl hee r
formalciozmepdud teivnitgcow e hsit chhpi asr timcoudilersale r l baytm eudt ual
simulCaotnisoenqt.uh neeon ttoil(foyu n n )solvnaobrtie ladiletlpyyeo nntdd ho ee s
4 P.V ANE MDEB OAS
model huasasel dl.ou wstIe ortd e ttuor inan nfo ramnaidln tusittoyiwlfvoe e r king,
relyoinwn hgah ta bse cokmneo wanst h"ei nesusseeon"fCt H iUaRlCT HHE'SSI S:
whatifeslev tteo re effbcety ci ovmep/uc tabanbeb r loewu igthththsi ecn oo fop neo eft he
frommaold Tehlbesa .sm iocd oecflo sm puttahteimosrnee lmvoaenits nhs eh ,et lbofe
usieafdn wdh enne edweetd e:at chhe set mooou dre lsastn utddh eenitrs hdaiss covery
becohmies [t2or3y,T h ve5a 9l]io.Cdf hi cuthryT' hse isssio sm etwhhiincgh cannot be
promvaetnh emaAttbi ectsahttle hl eycs.oi usl idn vbael biysd oamtceeo dn vincing
counterbeusxtofaa rmn pocl oeu,n terheabxsea emnp ldei Aslfoclro mvaelrfoiersd m.s
computhaabbvieelfoe iuntn tydso a stftiyht eh eWsewi isrl.el s tthreircoetufo rrsee lves
tom odfoerlws h iCchhcu hrT'hse hsoilsd s.
Whetnht eh eoocfro ym putcaotmipolnweaaxfolsiu tnydi entdh e early nineteen­
six[t4it3ehs]set uodmfya chmiondewe alrsse viMvoeddwe.hl ishc ahbd e sehno twon
bec omputaetqiuoinvabalellceyadn miteeff r eangta siinn,tc heeh ya ddi effrent
propewrirtteihse tpstoe i camtne sd p accoem plmeexaistAuylr asel osa .rc goel lection
onfe mwo dwealissn turcoebdda,so entd he ex peraindeden vceel oiptnmh weeon rtlsd
opfr acctoimcpaulTt hiennrogle .o nsgeeertm oebed au niforremol natsbiheitpw een
thvea rimooudsle iltkshe e raett hwleae sov egfle necroamlp uttahbeiAollrisyto.y,
clasmsaicchailn el imtkohedue ne alTrsuy r imnagc h[i2n12e03, ]a nMdi n'ssk y
multicmoaucnh[ti18en1,r9e1 ]tu ronuettdob et ouon wifoerlm doyd erleianlgi stic
computaantwdie orgners a dduiaslclaaysrv dieamdba lceh miondee ls.
Depenodnti honejbg e ocntlesi tkmoea sn ipiutnlh caeot mep ut(antuimolbnieskr es
nonneignatteiogvraeel r psh,a nsutmreitrnwimgocos d)e,l osb thaaaivd neoe mdi nant
posiitnmia ocnh inceo-mbpalsteehxdei otryy :
thoef fm-ullitnTierut iamnpagec h[]ilw,nh ei rcehp retshseetn atnsmd oadrfoedrl
• stringc-oomrpiuetnaatntedid o n,
threa ndomm aacc(hciRen)Aase Msis n trobdyCu ocoekd and[ 2Rw1ehc]ik,ch ho w
• modtehliesd eaVloiNnze eudm asntny le computer.
Buott hmeord weelrpser opaosws eealdnl wd e arcec epteadn dywi iffitchAuotlu tty .
thsea mtei mdeu,rt ihneega rnliyn eteeno-nbseee cvaeamnwetao irtfeeh fa sec, tt h at
somceo mplneoxtiistoeyne smt eohd a vame odel-imnedaenpTiehnnmegdo .es ntt
imporottfha ennstoe t icoonnsce trhcnehe adr actoecfro imzpautftiaeaostnii boinlailt y
ort ractability.
Ap robilssea tmibo dfe ae siibfcliabetnes olivpneo dl yntoimmiesa tl(afo atrtse h de
firtsitbm yeE dmo[n2ds6B ]ut)th .i s veryt orne oqttuihiooarnnte ie sd eeenmtsi fies
am achmiondoeen wl h itchhi si mste iamseuT rhceerd u.fac ciitans lo t wh iiifsct :a b ne
shotwhnra eta somnaacbhsliienm euesla acthe w oittphhoeilrny nobmoiuanld-etdi me
overihftloe latodwh,tsa hp tea rtcihcouoifalmc aoerd i etnlh fien idoteffiae osni biisl ity
irrealsle ovanasogn n tre,e mwaiinttshhr ieen ao lfr me asmonaacbhmlioend ee ls.
Afu ndamental proibntl heem n,ei andreiltsyec eonav-sews reeelivdtlse h, ne t ies
P= N?Pp robHleermPed. e notthceels a osfps r oblemsb yds eotlevrambilnei stic
Turmiancgh iipnno elsy ntoimmaienaN,dlP d enotthceels oa pfsr so bsloelmvbsay b le
nnodeterTmuirnmiianscgth iiicpnn o elsy ntoimmieaP.l= ? TNhqPeu esatsifokorsn
thpP-owoenfro ndetearrmteih nepirrseom bw:lh eimacsn h o ndetemramcihniinset ic
casno livnpe o lyntoimmiea,l c awnhnibocest ho livnep do lyntoimmibeay l
ar easodneatbelremm iancihSsittnaiedtc?iee ffrde natrnelo yn:d eterministic machines
feasifobrpl rea cctoimcpagul?t in
MACHIMNOED ELS SAINMDU LATIONS 5
Thfenu damecnotmapll celxaistsye s bPe caapnmadero tfaNf Pnu damental
hierLaOrGcShPyAN:CL EO,G SPAPC,NE PP,,S PAECXE,P TI.MA.En.,ad g ain
thefaocretydh p er obtlheeamat oc tfhh ecsleah sasasme as chined-edfienpietnidoenn,t
antdh eaffitc iseinmtu laarnteei eobdneesfod r ec aconln aeti hmta htec sleaa srsieen s
facmta chnidneep-eainndrdee nptr efusnednatm ecnotnacloe fpc tosm putational
complIestxe iettmhyse. r tehfocarotem pltehxeiaotsry yk w,ne oi wtto diabsya ,s ed on
thfoel loawsisnugm ption.
INVARITAHENSC"IESR :e aesm"oa ncahbcilasnnie msu loattwheie treaph a oiclnhy nomially
bounodveedr hteiaamdnea dc i onn tsaftcatonovre rihsnep aadc e.
Afu rtdheevre loaprmofresonemtt hs et uodpfya ralIltteu lrionsuemtd. that there
waasd eecpo nnebcettiw"oetnei nim pnea "r allealn "dms apcaihcsniee n"qe use ntial
modeTlhsri.es l aitksin oonaw stn h Pea raClolmeplu tTahteisoins .
PARALCLOEMPLU TATTIHOENSW IhSa: tceabvnsee o rl ivpneo dl ynboomuinsadplealdcy e
onar eassoenqaubmelanect hmiioandcleea b lne siopnlo vleydnb oomuintadilemldey on
ar easopnaarmbaallcelh eailnvn die c,e versa.
This dcehaawlpitstth eheer v nicdteeh eaxtii ssntu sp pootfrh vtea liotdfhi aetb yo ve
two tThhesest euosdf.sy i mulwaittpihoo lnysn ombioauln-odtveiedmr eih se ad
at radistujibeioccnntoa mlp lex(ist[ey17e ,5t 1, 8h3 e].To) hraeyd ditrieoqnuairle ment
ocf onstanotv-efarichnstep oaardcc oem plextioht ay vbese eelnea mrisgg enloyr ed.
Hoewvears, w wiesle ileSn e ct2ti,ho pinrs o bilnseo amtse asiymt aa syse eTmh.e
ParaClolmeplu tTahteihsoainrss e ceqiuvisetodem a et tenattfeiirowt na fi,sr st
formulbayGt oesldcd hl[a3g9e]r.
ThIevn ariTahneccseai nsi nbtee ripntr wewota eyds :
thoer thiondtoexr rperqeuttihaarats etiis ons ngil meu laacthiiboeonvbt eohsu nds on
• thoev erhienavdossli vmeudl taneously;
thlei bienrtaelr parlelfotorawa stt iiomne -esffiicmiuelananttad in eo nnt irely
• diffesrpeancte -seiffimcuil(eawnthtmii aoctynhu oruntt ro e qaum iurcleha reg.egr.,
exponoevnetriihanel a,td i me).
Web elitehvtaehto e r thiondtoexr pirste htceao etrcirto nt ooan deh etroe for
computcaotmipolneaxli Ctlye atorhlnieyeno, vr eyis.fst piaogcartet i ebmsoe u nded
complcelxaiistnsyde esp etnhdleei nbitenlrtyae,lr psrueffiticaoentsr i dtoeomnr a ke
thcel aisntsh efuesn damehnitearmlaa rcchhiyn e-iAnldmeaoplsseltin mduelnatt.i ons
onfien ditsnh lei tearcahtibueorvtoeevh e rhaettah sdeas m e Atliisimtouse s .e tfou l
stucdlya dsesfiensbe ysd i multtainmaeenos dup sab coeu nadnsd, o trhteh odox
interpirnsee teaditenoid ro dnte omr a kteh emsuell tei-prebsoouunrcdcleead s ses
machine-Sitnovcakr[m2i1e6ayh]neaa trsr. g tuheoadnt re e afosrou ns inTgu rtihneg
machmiondieetn lh fo eu ndaotcfio omnp ltehxeiioptsrry ye ctihsiienslv ya rtihaantc e
iptr ovides.
Thees ciadnpe eefn dtihnIevgn a riTahnecaseni ds P tahreaC lolmeplu tTahteisoins
icsl eparrelsiye ntn hwteo rrde asoTnhaiibessla seii.nl feyrfr roemtd h set andard
pracottfih tcehe e orceotmipcuatle r scienicitefas c cewodim etmvhui ndietnyc ew hen
agatihnvesat l iodtfih Itenay vr iaTnhceFeso iersx .a mwphleienn1, 7 94iw ta fosu nd