Readings in artificial intelligence : a collection of articles

550 Pages·1981·21.19 MB·English

by  Saul Amarel

READINGS
IN
ARTIFICIAL
INTELLIGENCE
a collecotfia ornt icblye s
AmarelB artsow BerlineBrlse doe BuchanaCnh ang Cohne Davis
• • • • • • •
Doyle Duda Erman Feignebaum FikesG aschgn iGreen Hart Hayes
• • • • • • • •
Haye-sRoht Lesser Mackowrth Manna McCarhty MitchelMlo oer
• • • • • •
NilssoPne arurtl Reddy ReiterS horet liSflfagleS tfiek
• • • • • •
WalidngerW eyhrauch WilkinWso ods
• • •
editbedy
BonneiL ynnW ebber
UniversoifPt eyn nsylvania
and
Nils]. N islson
StanforUdn iversity
MORGANK AUFMANN
PUBLISHEIRNSC,.
95F irsStt reeLto,sA ltoCsa,l ifor9n4i0a2 2
LibroafrC yo ngrCeastsa loging-in-DPautbal ication
Maine ntruyn dert itle:
Readingisna rtifiicnitaell ligence.
Includbeisb liograpahnidie nsd ex.
1.A rtifiicnitaell ligence-Addersessasyess,,
lectureIs.W.e bberB,o nniLey nn.I IN.i lsson,
NilJs .19,3 3-
Q335.5.R139 85 006.38 5-24203
ISBN0 -934613-03-6
Copyrig©ht 1 98M1o rganK aufmanPnu blisheIrnsc,.
95F irsStt .L,o sA ltosC,a lifor9n4i0a2 2
Allr ighrtess ervNeod .p arotf t hipsu blicatmiaoynb er eproduced,
storeidna retriesvyaslt emo,rt ransmititnea dn,y f ormo rb ya ny
means-electromneicch,a nicaplh,o tocopyirnegc,o rdinogr,
otherwise-witthhoepu rti owrr itten permoifst shiepo unb liesrh.
Printeidnt heU niteSdt ateosfA mericaL.i brarofyC ongress
CataloCga rdN umber8 1-31630.
ISBN0 -934613-03-6
(Previoupsulbyl ishbeydT iogPau blishiCnog. u nderI SBN
0-935382-03-8)
CDEFG-C-76
PREFACE
We regaradr tifiicnitaell lig(eAnIac)se a brancohf ther eacohf s tudenwtes ,h avea rrangweidt ht he
computsecri enwcheo seo bjectiistv oee ndowm a­ publisthoep rr inittf romp hotocopoifte hse origi­
chinewsi thr easonianngdp erceptaubaill itAire­s.n als ources-tshauvsi ntgh ec osotf r etypesetting.
tifiicnitaell liigsea ny coeu ndgi sciplBionreni. nt he
1905si,t g athermeodm entuma nda dolescceonnt­
Thep aperass semblheedr ceo vearv arieotfty o pics
fidenicnet he6 0sa,n db egatno m aturaen ds how
andv iewpoinStosm.ea ret heoretsiocmaele ,x per­
promisient he7 0sL.i kem anyo theyro ungs ub­
imentaMlo.s to ft he papaerrefs r equenctiltyeb dy
jectAsI,i sd iffitcout leta cahn dl earbne cauisthe a s
AI textbooaknsd currenrte searacrht icles. Al­
noty eta ccumulaatl eadr gbeo dyo fe stablitshhee­d
thougwhe might nboeta blteo g ivceo mpelling
oryA.l thougshe veraault hor(si ncludoinnego f
argumentfso re acho ft hep aperisn cludoerd
us-NJN)h avew rittAeInt extbootkhse,sb eo oks
againtshto se cnoontt aihneerde iwne, b elieve that,
gives omewhat differing poefrA sIp.Te oc tives
ont he whole,v oltuhmimesa yb ec onsiderreepd­
avoicdo mpledteep endenocne a nyo nep oinotf
resentaotfis voem eo ft heb estth inkianngd r e­
viewi,ti se ssentfioasrlt udentAsI t oosf u pplement
searcihnA I.
textbosotku dbyy r eadisnogm eo rigipnaaple rosn
AIt heorayn de xperimeTnhtep. u rposoeft his vol­
umei st om akea n umbeorf t hesiem portpaantp ers Weh aveo rganiztehedp apers fiivnetm oa jocrh ap­
morea ccessibleo-nnloytt o p reseanntd f uture tersS:e arcahn dS earcRhe presentatDieodnusc,­
tionP,r oblem-SolavnidnP lga nninEgx,p erSty s­
specialbiusttt osa ,l tlh osfeo rw hom thep roblems
ofa rtifiicnitaell ligheonlcdpe a rticuflaasrc inatitone msa ndA IA pplicatiaonndAs d,v anceTdop ics.
andi nterest. Eachs ectiiospn r ecedbeyda briedfe scripotfi on
thep aperistc ontaiAn ss.u bjeicntd eixsi ncluded
att hee ndo ft hev olume.
Manyo ft hep aperisn cludheedr aer er ather diffi­
cultto f indS.o mea ppearoerdi ginianll liym ited­
editicoonn ferepnrcoec eeditnhgasat r en owa vail­We thanakl olf t hea uthoarnsd p ublishfeorgrs i v­
ablien m icrofiocnhleyS .o mea rep ublishiencd o l­ ingu sp ermisstioor ne produtchee ipra pers.
lectioornj so urnatlhsa cto lleagned u niversliit­y
brarimeisg hhta vei ns ingcloep ioensl y-or none BonneiL ynnW ebber
whatsoevTeokr e.e pt hep ricoeft hev olumwei thin NilJs.N ilsson
vii
ACKNOWLEDGMENTS
Thee ditoarrsep leasteodt hantkh ef ollowaiun­g Reit,eR r.," On CloseWdo rldD ataB asesf,r"o m
thorasn dp ublishfeorrsp ermissitooni n clude LOGICA ND DATA BASES5,5 -7H6.,G allaainrde
copyrighted miantt heerp iraels evnotl ume: J.M inke(re sd).,P lenumP ress1,97 8.C opyright
1987 byP lenuPmr ess.
Amarel5,., " On RepresentaotfiP ornosb lemosf
ReasoniAnbgo utA ctionfsr,o"m M ACHINE IN­ MannaZ,. andR .W alidnge"rA, D eductiAvpe­
TELLIGENC3E, D .M ichi(eed .)p,a ge1s 317-11, proacthoP rograSmy nthesfirso,mA" C M TRANS­
EdinburUgnhi versPirteys 1s,9 68C.o pyrig1h96t8 ACTIONSO N PROGRAMMINGL ANGUAGES
byE dinburUgnhi versPirteys s. AND SYSTEMS2,(1 ):01-212A1C,M , 198Co0p.y ­
righ1t98 0b yt heA ssociatfioorCn o mputinMga ­
Gashcnig,J .",A ProbleSmi milarAiptpyr oach to
chinrey,I nc.
DevisiHnegu ristFiicrss:Rt e sultfsr,o"m P ROC.
6THI NTLJ.O INTC ONF.O N ARTIFICIIANLT EL­ WeyharuchR,. ",P rolegomteoan T ah eoroyfM ech­
LIGENCE3,0 -13071,97 9.C opyrig1h9t97 byI nter­ anizeFdo rmaRle asoninfgr,o"mA RTIFICIIANL­
nationJaoli nCto nferenocne sA rtifiIcnitaell li­TELLIGENC1E3,( 1,323)-:117109,8 0C.op yrig1h98t0
gence. byN orth-HollPaunbdl ishCion.g
Woo,dW. s A.," OptimSaela rcSht ratefgoiSrep se ech Dud,aR .,H artP., a nNd. N ils,s" oSunbjecBtaiyvee­
UnderstandCionngt rotlo,a "p peairnA RTIFICIAL siaMne thodfso rR ule-BaIsnefde rence Systems,"
INTELLIGENCCEo.p yrig1h98t1 b y North-Hol­inP ROCEEDING1S9 67 NATIONALC OMPUTER
lanPdu blishCion.g CONFERENCE1, 075-108A2F,IP Sv,o l4.5 ,1 976.
Copyrig1h97t6 b yA FIPPSr ess.
MackowrtAh.,," ConsisteinnNc eyt workosfR ela­
tionsf,r"o mA RTIFICIIANLT ELLIGENC8E(),1: 99- Green,C ., "ApplicatoifTo nh eorePmr ovintgo
11,81 977.C opyrig1h9t77 byN orth-HollPaunbd­ ProbleSmo lvingi,n"P ROC.l STI NTL JOINT
lishiCnog. CONE ON ARTIFICIIANLT ELLIGENC2E19,- 239,
BerelriH,n. ",T heB *T reSee arcAhl goritAh Bme:s t­ 1969.C opyrig1h96t9 b yI nternatJiooinanClto n­
ferencoensA rtifiIcnitaell ligence.
FirsPtr ooPfr ocedurfer,o"mA RTIFICIIANLT EL­
LIGENCE1,2 (213)-:401,99 7.C opyrig1h97t9 by
Hayse,P. ",T heF rameP robleamn dR elatPerdo b­
North-HolPluabnldi shCion.g
lemsi nA rtifiIcnitaell ligefnrcoemA, R"T IFICIAL
BldesoW.e ,W .," Non-ResoluTthieoonr ePmr ov­ AND HUMAN THINKING4,5 -5A9.,E lithaonrdn
ing,f"r omA RTIFICIIANLT ELLIGENC9E(,1 )3:51,- D.J one(se sd).,J ossey-B1a97s3s.C, o pyrig1h97t3
1977.C opyrig1h97t7 b yN orth-HolPluabnldi shingb yJ ossey-BIanscas.n, d E lsevSiceire ntPiufbilci sh­
Co. ingC ompan.y
Chagn,C .a nfd. S algl,e" UsinRge writiRnugl efso r Fiek,s RH.ar,t P., a ndN .N islos,n" Learnianngd
ConnectiGornap htso P rovTeh eoremsf,r"o mA R­ ExecutiGnegn eraliRzoebdo Ptl ansf,r"o mA RTI­
TIFICIAILN TELLIGENC1E2,2( ):91-5718,1 979. FICIAILN TELLIGENC3E(,4 ):2511-92278.C8 o,p y­
Copyrig1h97t9 b yN orth-HollPaunbldi shCion.g righ1t9 27 byN orth-HollPaubnldi shCion.g
ix
Walidnrg,eR .," AchieviSnegv erGaola lSsi multa­Dav,iR s.," InteracTtrinavsef eorf E xpertiAsce­:
neous,l"fy romM ACHINEI NTELLIGEN8C,E9 4- quisitoifoN ne w InfereRnuclee "s f,romA RTIFI­
136,E .E lcoacnkd D .M ichi(ee sd.)El,l Hiosr wood, CIALI NTELLIGENC1E2,() 2:211-517,1 979C.o py­
1977.C opyrig1h9t77 byE .W . Elcocakn dD .M i­ righ1t97 9b yN orth-HolPluabnldi shing Co.
chie/EHlolriwso odL,i mited.
McCarhty,] .a ndP. Hayse," SomeP hiloshoipcal
StfiekM,. ," Plannianngd M eta-Plagn,"n ifnrom Problems tfhreoS mt andpooifnA tr tifiIcnitaell li­
ARTIFICIIANLT ELLIGENC1E6(,)2 1:41-01,17 981. genc"e f,romM ACHINEI NTELLIGENC4E,4 63-
Copyrig1h9t8 b1y N orth-HollPaunbdl ishCion.g 502B,. MeltaznedDr . M ichi(ee d)s,.E dinburgh
UniversPirteys s1,9 69C.o pyrig1h96t9 b y Edin­
BarstoDw.,," A nE xperimeinnKt n owledge-Based
burgUhn iversPirteys s.
AutomatPirco grammgi,"n fromA RTIFICIIANL­
TELLIGENCE1,22 ():-71139, 1979.C opyrig1h97t9 Hayse,P. , "TheL ogiocf F ramse," fromF RAME
byN orth-HollPuabnldi shCion.g CONCEPTIONSA ND TEXTU NDERSTANDING,
D.M etzin(ge d).,d eG ruytepra,g e4s6 -6119,7 9.
Bucahna,nB .a nd E.F egienbaum," Dendraanld
Copyrig1h9t97 byW altedreG ruyt&er C o.
Meta-DendTrhaeliA:rp plicatDiiomnesn sni,of"r om
ARTIFICIIANLT ELLIGENC1E1,1( ,)25: -241,97 8. McCartyh,] ,." EpistemoloPgriocballe omfsA rtifi­
Copyrig1h9t87 byN orth-HollPaunbdl ishCion.g ciaIln tellig"e fnrcoemP, ROC.5 THI NTLJ.O INT
CONF.O N ARTIFICIIANLT ELLIGENC1E0,3 8-
ShoritffleE,., " ConsultaStyisotne mfso rP hysi­
1044,1 977.C opyrig1h97t7 b yI nternatJiooinnatl
ciasn",f romP ROC.C ANADIAN SOFC.O R COM­
ConferenocneA sr tifiIcnitaell ligence.
PUTATIONALS TUDIESO F INTELLIGENCE
McCarhty,] ,." CircumscriptFioornm-o AfN on­
(CSCSIU)n,i versoifVt iyc torViiac,t oBr.Ci.a, 1 980.
MonotonRieca soinng,f"r omA RTIFICIIANLT EL­
Copyrig1h98t0 b yC anadiaSno cieftoyrC ompu­
LIGENCE1,3 (1),2:27-3199,8 0C.o pyrig1h98t0 b y
tational SotfIu ndtieelsl igence.
North-HollPaunbdl ishCion.g
Dud,aR .G,a scnhgi,] .a ndP. Har,t" ModeDle sign
MooreR,.C .," ReasoniAnbgo utK nowledgaen d
int heP rospecCtoonrs ultSaynstt efmo rM ineral
Actino,"f romP ROC.5 TH INTL.J OINTC ONF.
Explora,t"fi roonmE XPERTS YSTEMSI NT HEM I­
ON ARTIFICIIANLT ELLIGENC2E2,3 -22179,7 7.
CROELECTRONIACG E,1 53-16D7.,M ichi(eed .),
Copyrig1h97t7 b yI nternatJiooinnCatol n ferences
EdinburUgnhi versPirteys 1s,97 9.C opyrig1h97t9
onA rtificIinatle lligence.
byE dinburUgnhi versPirteys s.
Eramn,L .,H ayes-Roth,L essre, and Reddy, Cohe,nP. andC .R .P earru,l" tElemenotfsa Plan­
F., V., D.
BaseTdh eoroyf S peecAhc t"s f,romC OGNITIVE
"TheH earsayS-pIeIe cUhn derstanding ISny­stem:
SCIENCE3,( )3:717-21129,97 .C opyrig1h97t9 b y
tegratKinnogw ledtgoeR esolUvnec erta,i"fn rtoym
AblePxu blishCionrgp oration.
COMPUTINGS URVEYS1 2(2)32-1251398,0 C.o py­
righ1t98 0b yt heA ssociatfioorCn o mputinMga ­ Dolye],,. " A TruthM aintenanScyes te"m f,rom
chine,rI ync. ARTIFICIIANLT ELLIGENC1E2(,3 ):-2237121,9 79.
Copyrig1h97t9 b yN orth-HolPluabnldi shCion.g
Wilki,Dn .s," UsinPga tterannsdP lanisn C hess,"
fromA RTIFICIIANLT ELLIGENC1E4(,)2 :615-203,M ithcelT.l,," G eneralizaastS ieoanrh c,"t oa ppear
1980C.op yrig1h98t0 b yN orth-HolPluabnldi shingi nA RTIFICIIANLT ELLIGENCCEo,p yrig1h98t1
Co. byN orth-HolPluabnldi shCion.g
x
Searcahn dS earch
1 I
Representations
Searcphr ocespsleasay f undamenrtoallie na rtifiinctiealll igIenfn acme­.
iliariozniensgew lift ah compleAxIs ystetmh,e raer es evertahli nognse
wouldw antt ok now that thoda ovw ei ths earcFhi.r sdto,e st hes ystem
uses earcahta llI?fs o,d oesi td o sob yb acktrackoirbn ygs ,c anning
breadth-ofrib resstt -fiWrhsatti? st hes earcshp aceW?h ath eurisatriec s
usedi no rderitnhges earcDho?e st hes ysteums ec onstrasiantti sfaction
techniqtuoeh se lrpe ducteh em agnituodfet hes earcMhu?c hi mportant
informataiboonus te aracnhd s earrcehp resentaitsci oonntsa iinnes dt an­
dardA I textbooaknsd,t hesteo piccosn tintuoeb es ubjecotfas c tive
researicnAh I .T hef ivpea perisn cludientd h isse ctiwoinli ln trodtuhcee
readetros omeo ft hei mportarnets earicshs ureesl atteosd e arch.
Amarelp'asp eirs a casset udoyn h ows hifitnsp roblerme presentation
cand rasticallyt hrese idzuoecf te h es earcshp acIet.i st hec lasspiacp er
ont hitso piacn dc ontaimnasn yi ntriguingf oicrdo enatsi nuriensge arch.
Theu seo fh eurisetsitci matfiunngc tifooncrso ntrolsleianrgrc ha istehse
questioofnh ow too btaitnh esfeu nctioGnass.c hnipga'pse ard dresses
thipsr obleimna c leaarn di nviting mlaanynieanrn g,i cfeo undatfioorn
futuwroer ki nt hiasr ea.
Woods'psa pevri ews recogansai s teiaornpc rho bleRma.t hetrh afno llow
theu suaalp proaocfhs earchfionrga minimal-pcaotshtt o a goaslt ate,
Woodss eektsh ef insatla twei tthh eh ighesscto r(er egardolfet shsec ost
oft hep atht ot hastt at.Ae p)plietdor ecogniptrioobnl emtsh,eh ighest­
scorisntga itse t(hceo nsistent) intoeftr hpepr eertcaetpitiounnap lud ta ta
thaitsm osts trongsluyp portbeydt hei npuetv idence.
Constraionntp so ssibplreo blesmo luticoannso ftebne u sedt or educe
thes izoef t hes earcshp acbee forsee arcbhe ginSso.m etimtehse sceo n­
straianrtess o c onfinitnhga vte rlyi ttsleear cehf foirsnt e edeadf tetrh e
constracionmtp utatiaorneps e rformIends .o mec asetsh,ec omplesteet
ofc onstraiisan stssu metdob ek nowna tt heo utsewth,i lien,o thecra ses,
constraairneta sc quiraendd i ntegraitnecdr emelnl.tyM aackwortpha'­s
perw,r ittseenv eryaela rasg op,r ovidaec sl eairn troducttoci oonns traint
satisfaacntdin oent worcko nsistaelngcoyr itIhtmi ssf. u ndamenttoau ln ­
derstandmionrger ecewnotr ki nt hiasr ea.
Mucho ft hee arlwyo rko nd evelopsienagr cmhe thodwsa sd onei nt he
conteoxfpt u zzle-soalnvdig nagm e-playCihnegs.hs a sp osepda rticularly
challengpirnogb lems. Bepralpiendree rs'csr iabnea sl goritchaml,l Be*d,
fors earchgianmge a ndp rootfr eeIsn.a ddititootn h eo ptimisbtoiucn d
ont hec osftu nction buyst ehdec lassiAc*aa llg oritBh*mu ,s eas pessi­
mistbiocu nda sw ell. Secaarnbc eht erminabteeldo twh osneo dewsh ose
boundcso nflict.
Wes haalnla liyndze et aas iple cpirfiocb olfet mr ansposrcthuaelntdigi­onI\)
th'em iisosnaarnicdea sn nipbraolbs(l'weh mi cihs sitnsa etcetd3)i -ononi r ­
........_
detroe valtuhaeetffe ec otfsa lterfonramtuilvaeot fti hopinrsso bolnet mh e
CJ)
expecetffiecdi eonfmc eyc hanpircoacle dfousrro elsvi itan,ng ad l sion order
)>
toe xaminper otchetesh sacetos m ien tpol awyh eant rsainttiaoknpe lsa ce:IJ
0m
froma g ivperno bfolremmu latiaob ne titnetrAof totenhreie .n ivteirabla Il
formulaotfi otmnh isesi onaarnidce asn nipbraolbsli ensm e ct3i,o nt h)>e
z
OnR epresentoafPt rioobnlsoe fm s probulnedme rfigvoceeh sa nignfe rosm ulaetaicoohnfw , h ich incre0a ses the
CJ)
ReasonaibnoguA tc tions easwei twhh iicctha bne s olvTehde.rs eoefr mulaatrideoi nssc uisns esde c­
)>
tio4nt so1 1A. s ummaorfty hm ea iind eiants h e evooflf roumtuiloan ti:IJo ns,
m0
andc ommeonntt sh peo ssiobfim leicthya ntihzteir nagn sibtetiwoenesIn
SauAlm arel formulaatrieo ngsii nsv eecnt1 i2o. n JJ
-u
RPrCiAn cLeatbono.r atories :IJ
PROBLMES OF REASONING ABOUT ACTIONS m
N.J.
A p2r. obolfer ames onaibnogau ctt i(oiSnmso 1n9,6 6i)gs i vientn e romfas n
mz
(J)
inistiitaula att ieornm,si intaula ats ieootfnf ae,s iabcltei aonnadss ,e otf m
�
INTRODUCTION constrairnetsstt rhtiaehcp tap lti coafab citliitothnytes a ;so kft hper oble6m
solvteofir n tidhs 'e b essetq'u eonfpc eer misascitbitlohenca sat tn r aonrsmf '-l
Th1pe.u rpoofts hepi asp ietsroc laysr oimfbea siiscs oufce hso oicfre e presen­
tatfiooprnr obloefm sr eaasboonauictnt gi Tohnegs e.n eprraolb olfer me ­ thien istiitaulia ntttihooten e rmsiintaula Itni otnh.i sw ess heacsltpliey oc ni,fz
(J)
presenitsca otnicoenwr intethdh ree latiboentswhdeiieepnffr ewnaty s of as ystoefpm r oducPt,wi hoenprsre,o bloefrm esa soanbionaugct t icoanbnse
naturfaorlmluyl aatnesddo lved.
fromulaatp irnogb tloea mp rob·lseoml svyisntagen mtd h eeffi ciewnictyh
whitchhe scyasbntee e xmp etcotfe iadns do luttoti hopenr oblAenum n.d er­ In theP ,sa by asstiecm deosfacs riitputaaittoo innpoe on i inntt i mieas
lisotfit nhbgea sfiaect uorfet shs ei tuaTthiebo ansf.iae ct urerse qaurier ed
stanodfi nrtgleh aet iobnesthwipepre onb floremmu laatnipdor no bsloelmv ­
form aking daebcoiausctit ointoshn acsta bne t akfreonm t hsei tuation.
ing effiicasip ernecrye qfuotirhs deie tsei gpnr oocfe tdhucaratean su tomati­
Wec aals li tuaas ttiaootnfne a tu(nraN e- satt)eT.h lea nguiang ew Nh­ich
calclhyo otsheme o s'ta pprorperpirnaettseae'to ifao pnr obl(hetemcy a n
staatredese scriicsba eldal neN d- stlaatneg uSaugcehl. a an guiadsge efi ned
finad' pooifvn ite owft' h e probmlaexmi mtsahilamltpy lt ihpfiere osc ess of
bys peyciintfghfo el low:i ng
findians go lount)i.
Manpyr obloefpm rsa ctiimcptaoalrn cep raorbelo efrm aess onaibnogu t (i ) noan -esmeptt0c y a ltlhebeda suinci vetrhssieesc;t o nttahien s
actiIonnt sh.ep sreo blaec mosu,ro sfae c tihoatnso b ef outnhd asta tis­ baseilce meoUnfi t nst eirne ssti t(uhtaeit nidoinvsit dhouejba elcst,s ,
fieas n umboefrs peiceicdfo nditAi foonrsm.a l doeftf hicnilisat siso n of thpel easc;)
(ii)a soefbt a spirce didceafitnefesoed rl emeonfUt (0srp operotfi es
problegmisvi entin hs n ee xste ctiinto hnce,o ntoefax g te necroanlc eptual
elemeannrdte sl atbietowneesle enm ents);
farmewoforrfk or mulatthiepnsrgeo blfeocmros m putEeverrsy.ed xaaym ples
(ii)i saeo tfr uloeffs ro matfiooernx presisnti hloean nsg uage.
ofr esaonianbgoa uctt iionncsl ude apnal iarnpntliraningope r, g ania zing
Ther uloeffs ro matdieotne rwmhienteah neN r- stlaatneg uiasag l neie ar
dninepra rettyTc,h. e arreme a neyx ampolfie nsdt ursiaanlmd iiltaprryo b­
languaat gweo,- dime(nrgspaiho)iln caanlg uoarig htea ,ss o me ofrotmh.e r
lemisnt hciast egsourcayhss, c hueldiansgs emabnldty r anspoprrtoa­tion
cesses, apd reosgirganamci onfmgop erurp t,l ananm iiinltga orpyet riaoent,c . Regarodftl hefesos rt ma kbeyan n e xpreisnas niN -osnt altaen gusaugcaehn,
expreismsse iaotnnot atshsaaeg tri tv en elemean tc eiprnrt oaUpi0enr htays
ort haagt i ven osfeu lbesmeeitn nUt 0as r ree laitnae s dep cifmiaendn er.
Thuasn,e xpresasniN o-ns tliaantna egg uhea s ltohgeii cnatle rproefat ation
Ther esearpcrhe senitentd h is pawpases rp onsorienpd a rbty t heA irF orcOeffi ce of
ScientRiefisce arcuhn,d eCro ntraNcutm ber F4(96 3)8- 11P8a4r.ot ft hiwso rkw as truper oposaibtoiauo tnb afsaeitcuo rfte h sei tuaAt fniiiostnee.(t op ssibly
A
donew hilteh ea uthowra so na visitaipnpgo intmaetnt th eC omputeSrc ienDceep art­ emp)to yfe xpressainNo -nsst laatuneag giecs a lalc eodn figurTahtei on.
m
mento ft heC arnegIines titoufTt eec hnoloPgiyt,t sbuPrag.hA ,tC arnegTieec ht.h is emptcoyn figurwaitbleilw o rni ttIennt hleo giinct erprae (tonant­ion,
A.
researwcahss ponsorbeydt heA dvanced ResPeraorjcehcA tgse ncoyf t heO fficeo ft he emp)tc yonfiguriasat cioojnnnu ctiooftn h et ruaes sermtaidobeny s
SecretoafrD ye fenusen deCro ntraNcutm bers o-146.
itcso mponeexnptr esTshieso enutsn .i oofnt wo configuraat ions is itself
configurIafta inf3od nac.ro en figtuirotanhset,nh euinriw oinl lwr bei tten derived dLeesAtc b reai f paetsiioabncl.te ai nodn (lAe)d te notthreeu le of
ex ex,
{3.A basdiecs crisp,ot fai nfN l-ns,ti aastc eo nfigurfraomtw ihoinac lhtl r ue actithoanrt e fteorA s.A ruolfea ctiiogsn i vent raasn ssicthieomna be­
stateambeontuthtsNe - st(ahttacet a bne e xprestshetede riomnfts hNe­ twemeinx ed desocfNr -ispttaitoenhss,a t sh afoaen l dl oiwfotir nm:g
staltaen gucaagbnee d) ri ecotbltya ionrde edr iTvheudasb. a sdiecs cription (A)S:;a d (sas);b�d (sb) (.22)
complcehtaerlayc atneN r-iszteHaset nec.e fowrest hhla r lefteoar n N-state
Thfeea siabclteAi iodsne finaesadt ransforfmraottmih Noe-n s tSaatt ote h e
byi ts dbeasscirci ption.
N-stsabIt.Afe i asp plaitse atd,h etnhn ee xNt- stwaitbleels bT.h reu (lAe )
Ad erived doefas nNc -rsitpaattoti neope no iinntt i mieasl isotfci nomg­
spectihficeeo sn diutnidoenr twhhaeip cphl icoafAt aitso ain ps e rmissible.
poufnaedt uorfe sNt -hset Caotmep.o ufeantdu arrees defineodft hien terms
Thiistso beer pirnaetst eofodwl s'l:Id f( saan)dd ( sabr)be o tsha titshfieend ,
basfiaect uraenstd,h eayri en tentdoce hda racstietruiazitenti holeni sg ht
thaep plicoafA ta itso ainp se rimssiAb dleer.id've esdc rdi(psti)sis ao tni sfied
oft he prcoobnlsetmrs aoti hnadttes c,i saibootnuhstle e gaolfpi rtoyp osed
iifit ts r uuen dtehrle o giicneatrlp rieotTnah.tre u (lAe)i mpoasr eess triction
acticoanben s m adWee.d enobtyde ( sa)d eridveesdc ritphtaiitso na sso­
ont hmea ppiAn:s g�a s bi,. iert.e sttrhideco tmsa oiftn h feae siabcltei on.
ciatweidta hnN -stsa.Tt heel anguiang ew hdiecrhid veesdc riptions are
Thu,gs iveNn- satnsa afot rew hiAc ihas f aesiabclteiA o cna,bn e a pplied
formutleiadas n e xtenosfti hNoe-n s tlaatneg uaangidiet cs, a ltlheeedx tended
ats ao nliytf h Ne- stsabtt hear te suflrottmsh aep plicoafAt hiaocsne rtain
descrilpatnigouSnau gceahl. a nguadgeefi nbieytsd h felo lonwg:i
compofuaentdu trheaastr se p eciinfid e(dsb ).
(ia)s eVtic altlheeedx tenudneidv ewrhseeVr,0e V1( htiissn ot
c Le{t( A)b}et h(enfi i)ts eeotfr uloefas c tiaonnlde {st } b et he saeltl of
necesasp arroipilenyrc l)u;ts hieeox ntenosfi coVon n 0 tcaoimn­s
possNi-bslteaT theess e.{(t A )s}p ecai rfieelsa otfid oinr eatctta inability
pounelde meonfit nestr e(sedtfi naibntl eer omfts h bea sic elements
betwteheeenl emoefn{s }t.Gs iv eann tyw sot astxes,11sf ro{ms t}h,Ne - state
inV 0)a,n pdo ssniebwel lye m(eonnttos b taifrnoambV l0et) h at
isr edciattltya ifrnoamSb zil afen odn liytfh eerxei asp tesr misascitbiloen
arues efdo r builldeivdneegls chrisig;ph t ion s •
in{( A)}t hcaattn a kSezt o s 1L1e•ut sd enobtyTe t hree laotfdi ieorcnat t tain­
(ii)as eotfn ewp redidceafitnefesoedr l emeonfVt 1(s rp operatnide s
abilTihteeyx .p1r ess:r:ssTi,a o sns etrhttashtN e - stsa,,ct aen ojcucseutar r lier
relatthiaotnr sea qreuedfi orerx pretshsceio nngsn tirnagi
thasn i np oa sseivbolleu otfti hoseny stTehmu.ts h,re e laTtr ieopnr esents
condiotfti hopenr so b)l;e m •
loctailmo er dfoerrt hsey stPe.m
(ii)i saeo tfr uloeffos r matfoiroe nx presisnti hoen sl anguage.
A trajefrcotmo rNya-s nt aState oa nN -stsabit asefi neis tequesn1sc,2 e,
The rouffl oerasmt iiotnnh liasn guaraiegd ee nwtiittchha olos fte h Ne- state
..,.S mo fN -stsautectshh as=t1S as,m =Sabn,fod r e acih,l < i�mS,;i s
languEaagceehx. p reisnts hieeox nt enddeesdc rliapntgiuhoaantgs he le oi gcal
driecattltya ifrnoambs l;e.F 1o•ra n yp aiorfN -stSaats,eb sw, e s atyh at
interproefat p artoipoonsa ibtoiauco ton m pofuaentdu irnae s ituaAt ion.
sbi sa ttaifnraobSmlai e af n odn lSy=a s bo rt heerxei ast trjsae ctforrosyma
deridveesdc ridp(tsi)ias os neo tfe xpresisni oetnxhste e nddeesdc ription if
tos bW.e d enotthere e laotfai otnt ainfraobmiS lati ost bby y s �as bT.h e
langu(taii gasec onfiguirantt hlieao nng )uI.ang t ehe lionegtripcraelt ation,
notiofoas n c heidcsul loets oe ntohteio ofatn rj aectioitrts yh ;se e queonfc e0
d(si)as c ojnuncotfit ohpner optoisotinhsaa trse p ecbiyfii etcdso nstituent z
actitohnaastr te a kienmn o vionvget rht erj aectory.
exepsrisons. :n
Nowa probloefrm e ansionagb oautc ticoannbs e f ormluatiend thme
Theru loefas c tiiontn h sey stPe smp eyc ipafo ssniebxsltie t ua(tenixotn iJ
systPe amsfo lloGwivse:n :lJ
int imwei trhe spteoac g ti vteinm ael )esa csfu na ctoifco enr tfaaeitnu res in m
(i )a nN -stlaatneg uage (/)
prevsiiottuuisao Tnhsce.o mploefxa i ptryo abbloeaumct t iiodsne st ermined m
(ii)an e xtenddeesdc rilpatnigouna ge z
byt he natthudiresep eonfd Tehnecirease.s equeanntadil aolcc aolm ponent
(iiia)s eotfr uloefas c tion �
insu cadh e pendTehnsece eq.u epnatriictsao ln cewrintdehed p endeonfc ies (vi)a ni niNt-isatlaa ntadet ermNi-nsatla te, 6'-i
the snietxutoa tnfi aeotnu orfes se queonfc epsa st sWiewt iunlaoltbt ie o ns. z
find sthhroet esscth e(druot lhese h toertsrjtae ctfoorrmy )ti hnei Nt-isatla t(/)e
concewrintsehud c dhe pendiennt chiiess paperp.a riTtcsh o en cleorcnaeld 0
tot htee rminal( fi Nsa-c shteaedtxueil af>etat lsl ). ,,
witthha em ouonflt o ccaoln ttehxaittns e edteodd e teramc ihnaeno gfae
The osfae lNtl- staptaerostr,ld ye urneddte hrre e laTt,di eofinna se psa ce'lJ
basfiaect ufrroem osniet utatoti hnoeen x t. :lJ
thwaetc atlhlNe - stsaptaeTc hese.e aforrca hs oluttrjiaeocntt oarkpyel sa ce0
In stpheec ifiocfaa r tuilooefna ctiaonNn -,s tiast eg iveno fai n tear ms CJJ
int hsipsa ce. r
mixdeed scrisp'wt,hi ioicnwshr itatsfe lonl ows: m
$'.
(/)
s'=ds(;s, ) (2.1) 1T hirse latiisov ne ry ctloot sheer elat'ieoanr liinetrr'o dubcyeC da rnap1 95)8a, n d
whersie s btahsedi ecs criopftt hieo nN -stda(st )ei ,s aiastnsdso ciatedde noteTd,i nh isl anguafogre s pace-ttiompeo loIgnyC .a rnap'csas e,T r(e presetnitmse
ordebert weent wow orlpdo intths aatr eo nt hes amet rajectory.
c.v
�
Commontlhyie,n iftroimaull aotfai opnr obloefr me asoanbionugt 4.F ORMULATIONF2 O FT HE M& C PROBLEM IN
actiiaosv n esr fboarlm ul.Ga itviteohnnie n ivteirafoblra mlu latthieorne, are ELEMENTARY SYSTEMS OF PRODUCTIONS ----
csaebvneue p sroeasdlsfN io-fbrsolmtrleua a lttnahegpte uria aonngbegdielx ntset h msee ynd sdetesoedcfpm r rl iuoapcdnttggiiPeou.otTs nanhh sae t tWyesdp heeafs rlocmlriu inslbe naecotdt2we .iW M oet &sn h tc ep ab rryso tpb eilcnaeis amfsy yisimtobnepfpguml rs t eot druacoitfgi hottnhfo(J)ml>sre w ard
::0
chiocoeft huein veUr1as eno dft hfeea tuirnte esr omfws h isciht uaatrieo nsN -stlaatneg uage. ()
descrciasbnte rdo inngflluyte hnaecm eo uonfetff otrhtia nste edieondr dteor Theu niveUr so0e ft hNe- stlaatuneag gceo nttahifoenl sl owbian:;gi cI
l>
fians do luitnti hofoenr mulaPt.H ieorinesa ni mpordteacnitps oiionnt elemse:n t z
0
wheprreo bsloelmv inigas ffep cotwbeeytdr h c ehi ocoefa p robrleepmr esen­ (i )N indivmiidm.u2 a,l ,s mt haartme i ssionaNr iinedsi vaind(J)du als
tatIinao dnd.i sttiroionmn,pg r oviemnpe rnotbsslo elmvp ionwmgea rry e sult c1 c, 2,, c thaart•c•e •a nN nibals, ml>
fromt hdei scoavneedxr yp loiotfra etgiuolnia nNr -isttisaeptsae Tc hede.i s­ (i)ai no b• j• .(e actN t r anspofarctia)ltt-iihtoyen b bkwo iatatch a rrying::0()
coveorfsy u crhe guliarsfi atciielbsiy at aptperidoa prtreep reseonft ationsc apakc,i ty I
N-stsaptaeWc ees .h aillsllt urtahteeps oei bnytd si scuisnds eitniagnti hle (i)it iwsop apcoei pnL tp•s fR o trh leet b fanakn d rtihgbeha tno kft he ::Dm
follosweicntagis oenqsu oefnfo crem utliaoonfas ne xtevnedresdoi fto hne rivreers pelcyt.i ve -0::0
m
MissioannaCdra yn nipbraolbsl em. The braesliacbt eitownese ne lbeamiseninU cta0 sr a esf oll:o ws (J)
m
(i )a tt;h aisss ocainia ntdeisv oird ubtaohlawe ti tah sppaocien t z
TRANSPORTATIONP ROBLEMS:I NITIAL FORMU LATION.
(exa:ma ptl e(PmL)1a ,s setrhttashtm e i ssimo1ni asr tyah te �
3F.1 • OF MP&RCO BLEMS let fnbka), 6-I
z
Mantyr ansposrcthaetdpiurolonib nlager pmers o bloefrm esa soanbionugt (ioin)t; h iinsd itchaaatnetis n diviiasdb uoaatlrh bdeo a(xtea mp:l e (J)
actiSouncpshr. o blceabmnes fo rmulaastf loeldo Gwisv.ae s ne otfs pace on(c ib.k a)s setrhttashtc e a nnci1ib soa nl btoh)ae.t
poinatnis n,i dtiisatlr iobfu toibojtneh cetpssoe i niatnns td,r ansportatAi soeontfe xpresosnifoeor en asci,hn divainddu afolontr eh b eo a(htte y
facilwiittgihie vsce anp acfiintadin eo sp;t ismeaqlu eonftc rea nsportatsipoeynct sih pfeo sitoifao lnlsi ntdhiev aindoduf ta hles )bp oraotvaib daessi c
betwteheen sppoaiscnuetc sh att ehramtdi inrsaitlb uotfoi bojnei cntt hse se descroifpa ts iiotnu ait.iiecto.h n a,r iazcaetnseN r-stTahtuets.h, ie n itial
poicnatbnsea ttawiintehvdoi uotl aas teoitfgn igv en coonnps otsrsaiibnltesN -stfoartt hee probclaebnmew ritatsfe lonl o:w s
M
intermdeidsitartioebfo u btjieocnt s.
& c
Ani nteri;eusbtciolnftag hs ests rea nsposrcthaetdpiurolonib nligets mh se s0=abtp (ib)a,t (PmL1,),a t(mPL2),., . ,.a tm(. , .,LP)a,t (PcL1,),
claosf's d ciufficlrto spsrionbgl'te ympsib,fyt i he'edM issiaonnCdaa rnineis­ at(c2....P, La )tc,(N, LP). (4.1)
balpsr'o bTlheimps.r obalpepme ars frienbq ouoeoknnsmt altyh ematical
rectrieoaInths a.as l sroe ceaitvteedn itnti hodeny namic prograTmhmteie nrgm Ni-nsatilaas tt et afirno(e4m d. 1 b)ys ubstpi tfRuo ptr tiL h nrgo ugh­
out.
liter(aeBtlulrmaean nDd r eyf19u6s2a,)n idn t hlei teroanct oumrpeu ter
Thvee rsbtaalt eomfte hnet problem ifnrodmuucleaostf ai tnoh ne
simuloafct oigonnpi rtoicvee(s iSsmeoasnn. Nd e we1l96l)1,T. h feo lloiwsi ng M
av erfobramlu laotfti h'oemn i ssiaonncdaa rnineipsbr aolbs(l'weec ma iltl extenddeescdr liapntggiewuo &hance arn eo n-eemxptteyno sfUi 0io isnn tro­
ducteodg ewtihtceher r tparionp earntrdie elsa ftoitroh enels e moeftn htiss
formulF1a)tT.ih ornme ies siieoasnn adr tcharneneis beaetlkocs r oas s
extenTshiceoo nm.p oeulnedm ientnh teesx tenosfUi 0ao rnde e finientd e rms
riv(aesyrf roml etbfhatent kot he brain)gAk.h bt o aiatsv aiwlhaibwclihel l
ofn otiiontn hNse- state lancgoumapgoeeul.ne dmT aehrnetetsh fseelo low­
holtdw poe opalnewd,h iccahbn e n avigbayat necydo mbinoafmt iiso­n
insgi sxu bsoeftt hste o ta{lm }o sfme its sioannatdrh iteeo sts ae{lct } o f
sionaanrcdia ensn iibnavloslo vnient gwop ore opIltfeh m.ei ssioonna ries
cannibals:
eitbhaenrok f rtihveoe r'r e,rn o uitnte h're i vaerroe,u tneurmeabdta ny
timbeyc annitbhacela sn,n iwbiaillnlsd ultgheea inirrtn oh paogpithce n­ {m}L={x{imX}aE,t( x,p)L};t hseu bosfme its sioantla erfite,s
dencaineddso a wawyi tthhm ei ssioFnianrtdihs eeis m.p lesto fs ched{umlhe={ xiXE{ma}t(, xp ,R);t} hseu bosfme its siieoasntr a irght,
crosstihnawgtisp l elr mailttlh mei ssioannacdra inensit boca rlosts hse {mh={xlx£o{n(mx },b, k )t}h;se u bosfme ti snsairoaibeosa trhbdeo at.
rivseaeryfl .
Inam orgee nervaelriszoieftodh pn ir so btlheemar,rNe e m issioannadr iesT hteh rreeem aicnoimnpgo eulnedm {ec nL}•t { sc h{,c ha rseu bsoeft st he
N canni(bweahrles� 3 N)a n tdh beo ahtaa sc apakc( iwhteyrk e� ). W2 e totsaeoltfc annibaldse ftiihnnaaes tdi maimrlaean rn er.
catlhlpi rso btlheMe m prbolemW.es harlelfet rot hsep ecpirfiocbt lheamt Int hMe probtlhepemr ,o tpieoerfis n tertehssetp efcoirfo ifpc eart­ion
weh avfoer mluataeb&cdo ( vhwee Nr= e 3 k,= 2)a tsh eel emenM taprryol be.m missai&cb ctl iaeor tnesh s ei zoefts h ceo mpoeulnedm tehnattsh avjeu st
&c \l''!
Thsei exl emeancttairtohynwa seth avjeu isntt rocdaubnceu e sdet do geert h
introidu.tcehe.ned u ,m boefer l emiennt thsseu bs{emt}sL , e{tmLcRe.}t ,
ML, MMbRC,,L C,R C,b d enotthneeu mebro fi ndiviintd huseae l{tsms } L, inc ertsaeiqnu etnofoc rems macro-tarcatnisosfenerstoi sfinfo ngrd ividuals
{m}.R,.,{ .chr especTthievaserevle ay r.i atbhlatetas kv ea lfruoemst he froomnr ei vbearnt kot hoet hAe trr.ae nros frfi ndivfirdolumeat florts i ght,
finsieottfne o ngnaetiitnveegJ e0r {s0 ,I 2,,. ,.N .}. Tihtneesgaeer raesl so wheIr� er;S kcabne e fftecebdya s equence
N =
elemoefnt thesex tenosfUi0 • oThne byr iwnigtt hh eimnt heex tednedse­d (LBL)('L,B; L )..'.,,( LBL)', (UBR)(',UB R)'..,. ( ,UB R)'
cripltainognut ahagere i thrmeeltai=tc,i> o,<n ,sa sw elalsc ompound '---- (MB LR)', .�
relatthiaotno sba traei frnoamtb hleevm it ah leo gciocanln ectives rt imes rt imes
- , V/\,, (4.2)
anadl tshoae r ithfumnecttii+co, n .s dAe ridveesdc rdi(sp )wt hiioicnsh
-
assocwiiatathnNe -ds tsaiatss e e otfe xpretshssaipoten ycsc i efrtaariint h­ This seoqfau cetniscotena wsri ttashne mpbtoya attl eafnted n dwsi tahn
metriecl abteitownteshev ena riMaLbM>lR ee•st wch.o vsael aureoesb tainede mpbtoyaa ttr ight.
froms . Wec avni etwh see queonfec lee mentariyn( 4a.ac2sta) it ornasn sfer
Ther uloeffs o rmatthiwaoetns h alflo drue ssec rliapntgiuoaanrgo eef s macroatchtiaicstoo nm peodos ft wpoa rtthsfie:r psatcr otn soifts htiesn i­
thtey pceo nventuisoeindnla olgltiyhc ey;yi ellidn eexaprr esEsxiporness.­ tial sleoqaudfoeirnntc ghbe eo aotre, q uivatlhueenn ltolayd ingf osre quence
sioanrcseo ncat(ewniasttehep da rcaotmimnatgsof ) o rcmo nfigurTahtei onst.hp el atcheai tst hoer igitnht er oafn Tshfesere .c opnadsr tt awritttshh e
basdiecs criptiin(4o 1.ni) as gn ei xvaemnop falc eo nfiguirnta htleii onne ar rivcerro sasniidns fog l lobwyea dnu nloasdeiqnugefo nrtc hebe o aotr,
language. equivablyte hnleto layds ienqgu foenrtc hepe l atcheia tsth dee stionfa tion
Thvee rsbtaalt eomfteh Mne t c probdloeenmso i tn duau cnei qcuheoi ce thter aenrSs.if ntchece o nstorfat ihpnert osb alregemi vientn e romfts h e
ofa s eotff a esiabcltei Woe&ns sh.ac loln sfiirdase' trr easosneoatfeb llee­' relatiovfve a rsisioezuotesfiss n divaitpd ouiatnlhtscas at bn ec onsiadse red
mentaacryt itohnaasrta e s sutmobe efd e saibalntedh saatty ti hsgefi vceonn ­ endosfl oad(iounrngo l ad)is negqnuceetsh,ei intrs e asotnoaa tbtleetm hpet
straoinbn otacsta paacnidt tyoh pneo ssmiobdloeefo peratthbieon agTth .e forumlatoifao cnt iaostn rsa nsbiettiwosenuescnp h o inWtesu .st eh ese
seotfp ermiascstiibioalssn e us b osfte htsi estt h atb eoc batna biyns epde ci­ consideriantt hifeoo rnumsl atoifaos neo tff a esicbolmep oaucntdit ohnast
fiyntgh aep proprreisattroein ct thrieeo lnasnt uimvboeefm r i ssioannadr iesa roen lsye nstiobt oiavceto nstraints.
canniibnta htlews ro i vbearna ksws e alsl' erno ute'. {( A) '}Cio:m poufnesdai balcet iionfn osr mulFa2tt hiaaotrns e e nvseit toi boat
{( A) '}E1l:e menfteabarlsyaei c tiionFn osr mulFa2tt ihoaantr s ee nsittoi l'ec onstraints,
boacto nstrIani nfottlhsle.o wtirnaignt issocnh e,m adteanoatnae rsb itrary
configutrhacatotim opnl aeb taesdsie cs croifpa tnaN i -osnt: a te Loaedm pbtoya attl ewfittr ih n diidvuall rs�,k, ' (UBL)'.
Herweeh avaec laosfts r anssicthieom�nac sa bnte sh paetc aisfifo eldl ows:
Loabdo aattl efotni,en divaitad t uiam(lLe B L)'
Foarn iyn divxi,d ual Foars eotfr i ndivxi1d•,•u .,ax l,w,sh eIr� er ;S,k 0z
(LBL)a',a: t (PbLk)>a, t (PxL,)( ;M b+cb �k l>� a,a tb(P bL,) (L'B:L )a't( b>Pk L),a t(,x 1 ..a ,t (PxL,;),( M+Cb=O)� ::Dm
- a, pi). , b ""O
on(xk),;A b atb(kP >L )o,n (xb1k>.) .,,. o n(xb,k,) ; :n
a, A m
Movbeo aatc rotshrsef rferrol me tfotr ig(hMtB LR)' (/)
Int hetsrea nsiri tsti honenu sm,b oefir n divfirdoutmah llees bf atn tkh atm
(MBLR)a',a: t (kb>PL()Mb;+ Cb>O)� at,.(b.,pR)A; z
a, boardb otafhtoae rc rossing.
Unloada trb ioga,oht nt ien divaitad t uiam(lUe BR)'. �
Foarn iyn divx,i dual Movbeo a(tol adweidt rih n vdiiduaaclrsot)sh sre i vferrol me tfort i gahntd 6'-i
z
(U B R)':a t(PbRk)>o, n (bxk,) A;� at(,Pb Rk)a t(PxR,)A ; unloaalidlt p sa snsgeeartsr ig(hMBt L R+U 'BR.) ' (/)
a, ex,
0
Ina ddiwteih oanvt,eh t eh rfoelel oweilnegm eancttaiironyn s){ '('}ALi o ad Here waehl asvoec laao sfts r anssicthiewomhnai sic dshe finaesfod l lo:w s,,
"U
boaattr igohntie n divaitadt uiam(lLe BR )'',M obvoea atc rtohsresi ver Foar serti ndofi vxi1d,u ,ax ,l,Is� r�k, :n
fromr igtholt e (fMtB RL)a'n,'d U naldbo oaattl eto fnien divaitad ual ( BML R+ U'B R)a'[ :e] ,a t•(•P•b L)ko,,n (bx)k1., .. , o n(xb,k;,) a[ e], 0ro
A� r
ti(meUB L)T'h.de e finiotfti hoeanscset iaornes obfrtoamti hnpeer de vious atb(kP >R )a,t (PxR1),., .., a t(,,Px R;)A , m�
definibtysi uobnsst iLtfo urpt aRinnpdRg fo prp L nit hceo rrespaocntdiionngs . (/)
whear ee[] s tafonrd sca o nfigutrhaatctio otninrss a ibnyte hdce o ndiet,i on
Foerx amtphldeee ,fi niotf(i MBo RnL )i'as,s fo llows:
whiicshfo alslo nwoes x:p reisntsh ifeoo nro mn( yb,)k fo, ra niyn divyi dual
(MB RL)':a t(PbRk);>( Mb+Cb>O)a�,a tb(kP ,L) A; isi ncliund eTdh iissa w ayo fs ayitnhgaa tf,tt ehrce r ossailnl g,t hU1e
a, a. r