Solving Hard Problems for the Second Level of the Polynomial Hierarchy: Heuristics and Benchmarks

Recent research on answer set programming (ASP) systems, has mainly focused on solving problems more efficiently. Yet, disjunctive logic programs allow for expressing every problem in the complexity classes and . These classes are widely believed to be strictly larger than , and several important AI problems, like conformant and conditional planning, diagnosis and more are located in these classes. In this paper we focus on improving the evaluation of / -hard ASP programs. To this end, we define a new heuristic and describe its implemention in the (disjunctive) ASP system DLV. The definition of is geared towards the peculiarites of hard programs, while it maintains the benign behaviour of the well-assessed heuristic of DLV for problems. We have conducted extensive experiments with the new heuristic. significantly outperforms the previous heuristic of DLV on hard 2QBF problems. We also compare the DLV system (with ) to the QBF solvers which performed best in the QBF evaluation of 2004. The results of the comparison indicate that ASP systems currently seem to be the best choice for solving / -complete problems. 1Department of Mathematics, University of Calabria. 87030 Rende (CS), Italy E-mail: ricca, faber, leone@mat.unical.it 2Funded by an APART grant of the Austrian Academy of Sciences. Acknowledgements: This work was supported by the European Commission under projects IST2002-33570 INFOMIX, and IST-2001-37004 WASP. Copyright c 2005 by the authors 2 INFSYS RR 1843-05-09

[1]  Georg Gottlob,et al.  Disjunctive datalog , 1997, TODS.

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

[3]  Georg Gottlob,et al.  Default Logic as a Query Language , 1997, IEEE Trans. Knowl. Data Eng..

[4]  Yuliya Lierler,et al.  Cmodels-2: SAT-based Answer Set Solver Enhanced to Non-tight Programs , 2004, LPNMR.

[5]  Jia-Huai You,et al.  Unfolding partiality and disjunctions in stable model semantics , 2000, TOCL.

[6]  Rina Dechter,et al.  Propositional semantics for disjunctive logic programs , 1994, Annals of Mathematics and Artificial Intelligence.

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

[8]  Danny De Schreye,et al.  Answer Set Planning , 1999 .

[9]  Francesco Scarcello,et al.  Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation , 1997, Inf. Comput..

[10]  Peter Szolovits,et al.  What Is a Knowledge Representation? , 1993, AI Mag..

[11]  Toby Walsh,et al.  Beyond NP: the QSAT phase transition , 1999, AAAI/IAAI.

[12]  Wolfgang Faber,et al.  Pushing Goal Derivation in DLP Computations , 1999, LPNMR.

[13]  Chitta Baral,et al.  Knowledge Representation, Reasoning and Declarative Problem Solving , 2003 .

[14]  Fangzhen Lin,et al.  ASSAT: computing answer sets of a logic program by SAT solvers , 2002, Artif. Intell..

[15]  Timo Soininen,et al.  Extending and implementing the stable model semantics , 2000, Artif. Intell..

[16]  Burkhard Monien,et al.  A Distributed Algorithm to Evaluate Quantified Boolean Formulae , 2000, AAAI/IAAI.

[17]  Stefan Woltran,et al.  Comparing Different Prenexing Strategies for Quantified Boolean Formulas , 2003, SAT.

[18]  Reinhold Letz,et al.  Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas , 2002, TABLEAUX.

[19]  Wolfgang Faber,et al.  Experimenting with Heuristics for Answer Set Programming , 2001, IJCAI.

[20]  Armin Biere,et al.  Resolve and Expand , 2004, SAT.

[21]  Gerald Pfeifer,et al.  Enhancing disjunctive logic programming systems by SAT checkers , 2003, Artif. Intell..

[22]  Georg Gottlob,et al.  The Complexity of Logic-Based Abduction , 1993, STACS.

[23]  Marco Schaerf,et al.  Experimental Analysis of the Computational Cost of Evaluating Quantified Boolean Formulae , 1997, AI*IA.

[24]  Jussi Rintanen,et al.  Constructing Conditional Plans by a Theorem-Prover , 1999, J. Artif. Intell. Res..

[25]  Sharad Malik,et al.  Towards a Symmetric Treatment of Satisfaction and Conflicts in Quantified Boolean Formula Evaluation , 2002, CP.