The Impact of Treewidth on ASP Grounding and Solving

In this paper, we aim to study how the performance of modern answer set programming (ASP) solvers is influenced by the treewidth of the input program and to investigate the consequences of this relationship. We first perform an experimental evaluation that shows that the solving performance is heavily influenced by the treewidth, given ground input programs that are otherwise uniform, both in size and construction. This observation leads to an important question for ASP, namely, how to design encodings such that the treewidth of the resulting ground program remains small. To this end, we define the class of connection-guarded programs, which guarantees that the treewidth of the program after grounding only depends on the treewidth (and the degree) of the input instance. In order to obtain this result, we formalize the grounding process using MSO transductions.

[1]  Fangzhen Lin,et al.  Answer Set Programming Phase Transition: A Study on Randomly Generated Programs , 2003, ICLP.

[2]  Enrico Pontelli,et al.  SmodelsA - A System for Computing Answer Sets of Logic Programs with Aggregates , 2005, LPNMR.

[3]  G. S. Tseitin.  On the Complexity of Derivation in Propositional Calculus , 1983 .

[4]  Mario Alviano,et al.  Advances in WASP , 2015, LPNMR.

[5]  Hector J. Levesque,et al.  Generating Hard Satisfiability Problems , 1996, Artif. Intell..

[6]  Marius Thomas Lindauer,et al.  Potassco: The Potsdam Answer Set Solving Collection , 2011, AI Commun..

[7]  Bruce A. Reed,et al.  Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width , 2003, J. Algorithms.

[8]  Martin Gebser,et al.  Advances in gringo Series 3 , 2011, LPNMR.

[9]  Andrew G. Glen,et al.  APPL , 2001 .

[10]  Stefan Szeider,et al.  On Fixed-Parameter Tractable Parameterizations of SAT , 2003, SAT.

[11]  Stefan Rümmele,et al.  Tractable answer-set programming with weight constraints: bounded treewidth is not enough* , 2010, Theory and Practice of Logic Programming.

[12]  Johannes Klaus Fichte,et al.  Clause-Learning Algorithms with Many Restarts and Bounded-Width Resolution , 2011, J. Artif. Intell. Res..

[13]  Miroslaw Truszczynski.  Trichotomy and dichotomy results on the complexity of reasoning with disjunctive logic programs , 2011, Theory Pract. Log. Program..

[14]  Martin Gebser,et al.  Conflict-driven answer set solving: From theory to practice , 2012, Artif. Intell..

[15]  Victor W. Marek,et al.  Stable models and an alternative logic programming paradigm , 1998, The Logic Programming Paradigm.

[16]  Stefan Woltran,et al.  Answer Set Solving with Bounded Treewidth Revisited , 2017, LPNMR.

[17]  Fangzhen Lin,et al.  A Model for Phase Transition of Random Answer-Set Programs , 2016, TOCL.

[18]  Bruno Courcelle,et al.  Graph Structure and Monadic Second-Order Logic - A Language-Theoretic Approach , 2012, Encyclopedia of mathematics and its applications.

[19]  Alasdair Urquhart,et al.  Formal Languages]: Mathematical Logic--mechanical theorem proving , 2022 .

[20]  Martin Gebser,et al.  Answer Set Solving in Practice , 2012, Answer Set Solving in Practice.

[21]  Georg Gottlob,et al.  Complexity and expressive power of logic programming , 2001, CSUR.

[22]  Wolfgang Faber,et al.  The DLV system for knowledge representation and reasoning , 2002, TOCL.

[23]  Georg Gottlob,et al.  Bounded treewidth as a key to tractability of knowledge representation and reasoning , 2006, Artif. Intell..

[24]  Stefan Szeider,et al.  Backdoors to Tractable Answer-Set Programming , 2011, IJCAI.

[25]  Simona Perri,et al.  I-DLV: The new intelligent grounder of DLV , 2017, Intelligenza Artificiale.

[26]  Miroslaw Truszczynski,et al.  Answer set programming at a glance , 2011, Commun. ACM.

[27]  Bruno Courcelle,et al.  Upper bounds to the clique width of graphs , 2000, Discret. Appl. Math..

[28]  P. Gács,et al.  Algorithms , 1992 .

[29]  Georg Gottlob,et al.  On the computational cost of disjunctive logic programming: Propositional case , 1995, Annals of Mathematics and Artificial Intelligence.