SAT in AI: high performance search methods with applications PDF
Preview SAT in AI: high performance search methods with applications
SATinAI Introduction SAT in AI: high performance search SAT methods with applications MAXSAT #SAT SSAT SMT JussiRintanen Conclusion DepartmentofInformationandComputerScience References AaltoUniversity Helsinki,Finland IJCAI2013,Beijing SAT and NP-complete problems in Artificial Intelligence SATinAI Introduction SAT Earlier,NP-completeproblemswereconsideredpractically MAXSAT #SAT unsolvable,exceptinsimplestinstances. SSAT BreakthroughsinSATsolvingfrommid-1990’son. SMT Leadingtobreakthroughsinstatespacesearch(with Conclusion applicationsinconstructionofintelligentsystems.) References Startingtohaveimpactinotherareas,includingprobabilistic reasoningandmachinelearning. Why you needed to know about NP-hardness Garey&Johnson,ComputersandIntractability,1979 SATinAI Introduction SAT MAXSAT #SAT SSAT SMT Conclusion References Why you needed to know about NP-hardness Garey&Johnson,ComputersandIntractability,1979 SATinAI Introduction SAT MAXSAT #SAT SSAT SMT Conclusion References Why you needed to know about NP-hardness Garey&Johnson,ComputersandIntractability,1979 SATinAI Introduction SAT MAXSAT #SAT SSAT SMT Conclusion References NP-completeness has changed SATinAI Introduction Earlier: “ItisNP-complete,don’tbothertryingtosolveit.” SAT MAXSAT Now: “ItisNP-complete,youmightwellsolveit.” #SAT SATnowhasseveralindustrialapplications,andmoreare SSAT emerging. SMT Conclusion ExtensionsofSATareatopicofintenseresearchin References automatedreasoningandAI. ManyimportantproblemsinAIandCSareNP-complete: Combinatoricsoftherealworld(toomanyoptionstodothings). Howtodosomethingoptimally? Applications of SAT in Computer Science SATinAI reachabilityproblems Introduction model-checkinginComputerAidedVerification[BCCZ99]of SAT sequentialcircuitsandsoftware MAXSAT planninginArtificialIntelligence[KS92,KS96] #SAT discreteeventsystemsdiagnosis[GARK07] SSAT integratedcircuits SMT Conclusion automatictestpatterngeneration(ATPG)[Lar92] equivalencechecking[KPKG02,CGL+10,WGMD09] References logicsynthesis[KKY04] faultdiagnosis[SVFAV05] biologyandlanguage haplotypeinference[LMS06] computingevolutionarytreemeasures[BSJ09] constructionofphylogenetictrees[BEE+07] Classification of Problems by Complexity SATinAI Introduction SAT MAXSAT problem class searchspace #SAT SAT findasolution NP trees SSAT SMT findasolution NP SMT MAX-SAT findbestsolution FPNP Conclusion #SAT howmanysolutions? #P,PP References SSAT ∃−∀−Ralternation PSPACE and-ortrees QBF ∃−∀alternation PSPACE Differences in NP-hardness SATinAI MostscalablemethodsareforsatisfiableinstancesofSAT(NP). Introduction Thesecanbesolvedbecauseofgoodheuristics: solversare SAT successfullyguessingtheirwaythroughanexponentiallylarge MAXSAT searchspace. #SAT SSAT Currently,thesamedoesnot(asoften)holdfor SMT unsatisfiableinstances: determiningthatnosolutionsexist Conclusion References optimization: findingbestsolutions problemsinvolvingcountingmodels,e.g. probabilistic questions problemsinvolvingalternation∼and-ortrees Progressinthesequestionsismade,butithasbeenslower. NPsubstantiallyeasierthanco-NP,#P,FPNP,... Propositional logic Syntax SATinAI LetX beasetofatomicpropositions. Introduction 1 ⊥and(cid:62)areformulae. SAT 2 xisaformulaforallx∈X. MAXSAT #SAT 3 ¬φisaformulaifφis. SSAT 4 φ∨φ(cid:48) andφ∧φ(cid:48) areformulaeifφandφ(cid:48) are. SMT Conclusion φ→φ(cid:48) isanabbreviationfor¬φ∨φ(cid:48). References φ↔φ(cid:48) isanabbreviationfor(φ→φ(cid:48))∧(φ(cid:48)→φ). Forliteralsl∈X∪{¬x|x∈X},complementlisdefinedby x=¬xand¬x=x. Aclauseisadisjunctionofliteralsl ∨···∨l . 1 n
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