A Model for Phase Transition of Random Answer-Set Programs

ISCAS OpenIR

	A Model for Phase Transition of Random Answer-Set Programs
	Wen, L; Wang, KW; Shen, YD; Lin, FZ
	2016
发表期刊	ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
ISSN	1529-3785
卷号	17 期号:3
摘要	The 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.; The 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.
收录类别	SCI
关键词	Answer Sets Random Logic Programs Phase Transition
部门归属	Griffith Univ, Sch Informat & Commun Technol, Nathan, Qld, Australia. Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing, Peoples R China. Hong Kong Univ Sci & Technol, Dept Comp Sci, Kowloon, Hong Kong, Peoples R China.
语种	英语
WOS记录号	WOS:000380019200008
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/17320
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Wen, L,Wang, KW,Shen, YD,et al. A Model for Phase Transition of Random Answer-Set Programs[J]. ACM TRANSACTIONS ON COMPUTATIONAL LOGIC,2016,17(3).
APA	Wen, L,Wang, KW,Shen, YD,&Lin, FZ.(2016).A Model for Phase Transition of Random Answer-Set Programs.ACM TRANSACTIONS ON COMPUTATIONAL LOGIC,17(3).
MLA	Wen, L,et al."A Model for Phase Transition of Random Answer-Set Programs".ACM TRANSACTIONS ON COMPUTATIONAL LOGIC 17.3(2016).

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