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dc.contributor.authorWen, Lian
dc.contributor.authorWang, Kewen
dc.contributor.authorShen, Yi-Dong
dc.contributor.authorLin, Fangzhen
dc.description.abstractThe critical behaviors of NP-complete problems have been studied extensively, and numerous results have been obtained for Boolean formula satisfiability (SAT) and constraint satisfaction (CSP), among others. However, few results are known for the critical behaviors of NP-hard nonmonotonic reasoning problems so far; in particular, a mathematical model for phase transition in nonmonotonic reasoning is still missing. In this article, we investigate the phase transition of negative two-literal logic programs under the answer-set semantics. We choose this class of logic programs since it is the simplest class for which the consistency problem of deciding if a program has an answer set is still NP-complete. We first introduce a new model, called quadratic model for generating random logic programs in this class. We then mathematically prove that the consistency problem for this class of logic programs exhibits a phase transition. Furthermore, the phase-transition follows an easy-hard-easy pattern. Given the correspondence between answer sets for negative two-literal programs and kernels for graphs, as a corollary, our result significantly generalizes de la Vega's well-known theorem for phase transition on the existence of kernels in random graphs. We also report some experimental results. Given our mathematical results, these experimental results are not really necessary. We include them here as they suggest that our phase-transition result is more general and likely holds for more general classes of logic programs.
dc.publisherAssociation for Computing Machinery, Inc.
dc.relation.ispartofjournalACM Transactions on Computational Logic
dc.subject.fieldofresearchArtificial intelligence
dc.subject.fieldofresearchPure mathematics
dc.titleA Model for Phase Transition of Random Answer-Set Programs
dc.typeJournal article
dc.type.descriptionC1 - Articles
dc.type.codeC - Journal Articles
gro.facultyGriffith Sciences, School of Information and Communication Technology
gro.hasfulltextNo Full Text
gro.griffith.authorWen, Larry
gro.griffith.authorWang, Kewen
gro.griffith.authorShen, Yi-Dong

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