5 CONSTRAINT SATISFACTION PROBLEMS
5CONSTRAINTSATISFACTIONPROBLEMSInwhich weseehowtreatingstatesasmore thanjustlittleblack boxesleadsto theinventionofa range ofpowerfulnew search methodsanda deeperunderstandingofproblemstructure and4 exploredtheideathatproblemscanbesolvedby searchinginaspaceofstates. Thesestatescanbeevaluatedbydomain-specif icheuristicsandtestedtoseewhetherthey ,however,eachstateis is representedbyanarbi-BLACKBOXtrarydatastr ucturethatcanbeaccessedonlybytheproblem- specificroutines thesuccessorfunction,heuristicfunction, , whosestatesandgoaltestconformtoa standard,structured,andverysimplereprese ntation( ).Searchal-REPRESENTATIONgorithmscanbede finedthattake advantageofthestructureofstatesandusegen eral-purposeratherthanproblem-specifiche uristicsto enablethesolutionoflargeproblems( ).Perhapsmostimportantly, thestandardrepresentationofthegoaltestre vealsthestruc-tureoftheproblemitself( ).Thisleadstomethodsforproblemdecomposit ionandtoanunderstandingoftheintimateconn ectionbetweenthestructureofa ,aconstraintsatisfactionproblem(orCSP)is definedbya setofvari-CONSTRAINTSATISFACTIONPROBLEMa bles,X1; X2; : : : ; Xn, anda setofconstraints,C1; C2; : : : ; Cm.
INFINITE DOMAINS Discrete variables can also have infinite domains—for example, the set of integers or the set of strings. For example, when scheduling construction jobs onto a calendar, each job’s start date is a variable and the possible values are integer numbers of …
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