Abstract
Recent research on answer set programming (ASP) systems, has mainly focused on solving NP problems more efficiently. Yet, disjunctive logic programs allow for expressing every problem in the complexity classes \(\Sigma^P_2\) and \(\Pi^P_2\). These classes are widely believed to be strictly larger than NP, and several important AI problems, like conformant and conditional planning, diagnosis and more are located in this class.
In this paper we focus on improving the evaluation of \(\Sigma^P_2\)/\(\Pi^P_2\)-hard ASP programs. To this end, we define a new heuristic h DS and implement it in the (disjunctive) ASP system DLV. The definition of h DS is geared towards the peculiarites of hard programs, while it maintains the benign behaviour of the well-assessed heuristic of DLV for NP problems.
We have conducted extensive experiments with the new heuristic. h DS significantly outperforms the previous heuristic of DLV on hard 2QBF problems. We also compare the DLV system (with h DS ) to the QBF solvers SSolve, Quantor, Semprop, and yQuaffle, 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 \(\Sigma^P_2\)/\(\Pi^P_2\)-complete problems.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This work was supported by the European Commission under projects IST-2002-33570 INFOMIX, and IST-2001-37004 WASP.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Lifschitz, V.: Answer Set Planning. In: Schreye, D.D. (ed.) ICLP 1999, Las Cruces, New Mexico, USA, pp. 23–37. The MIT Press, Cambridge (1999)
Eiter, T., Gottlob, G., Mannila, H.: Disjunctive Datalog. ACM TODS 22, 364–418 (1997)
Rintanen, J.: Improvements to the Evaluation of Quantified Boolean Formulae. In: Dean, T. (ed.) IJCAI 1999, Sweden, pp. 1192–1197 (1999)
Eiter, T., Gottlob, G.: The Complexity of Logic-Based Abduction. JACM 42, 3–42 (1995)
Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. CUP (2002)
Leone, N., Rosati, R., Scarcello, F.: Enhancing Answer Set Planning. In: IJCAI 2001 Workshop on Planning under Uncertainty and Incomplete Information, pp. 33–42 (2001)
Janhunen, T., Niemelä, I., Simons, P., You, J.H.: Partiality and Disjunctions in Stable Model Semantics. In: KR 2000, pp. 12–15, 411–419 (2000)
Koch, C., Leone, N., Pfeifer, G.: Enhancing Disjunctive Logic Programming Systems by SAT Checkers. Artificial Intelligence 15, 177–212 (2003)
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV System for Knowledge Representation and Reasoning. ACM TOCL (2005) (to appear)
Simons, P., Niemelä, I., Soininen, T.: Extending and Implementing the Stable Model Semantics. Artificial Intelligence 138, 181–234 (2002)
Lin, F., Zhao, Y.: ASSAT: Computing Answer Sets of a Logic Program by SAT Solvers. In: AAAI 2002, Edmonton, Alberta, Canada. AAAI Press / MIT Press (2002)
Lierler, Y., Maratea, M.: Cmodels-2: SAT-based Answer Set Solver Enhanced to Non-tight Programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 346–350. Springer, Heidelberg (2003)
Faber, W., Leone, N., Pfeifer, G.: Experimenting with Heuristics for Answer Set Programming. In: IJCAI 2001, Seattle, WA, USA, pp. 635–640 (2001)
Cadoli, M., Giovanardi, A., Schaerf, M.: Experimental Analysis of the Computational Cost of Evaluating Quantified Boolean Formulae. In: AI*IA 1997, Italy, pp. 207–218 (1997)
Gent, I., Walsh, T.: The QSAT Phase Transition. In: AAAI (1999)
Narizzano, M., Tacchella, A.: QBF Solvers Evaluation page (2002), http://www.qbflib.org/qbfeval/index.html/
Berre, D.L., Simon, L., Tacchella, A.: Challenges in the QBF Arena: the SAT’03 Evaluation of QBF Solvers. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 468–485. Springer, Heidelberg (2004)
Marek, W., Subrahmanian, V.: The Relationship between Logic Program Semantics and Non-Monotonic Reasoning. In: ICLP 1989, pp. 600–617. MIT Press, Cambridge (1989)
Leone, N., Rullo, P., Scarcello, F.: Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics and Computation. Information and Computation 135, 69–112 (1997)
Baral, C., Gelfond, M.: Logic Programming and Knowledge Representation. JLP 19/20, 73–148 (1994)
Ben-Eliyahu, R., Dechter, R.: Propositional Semantics for Disjunctive Logic Programs. AMAI 12, 53–87 (1994)
Faber, W., Leone, N., Pfeifer, G.: Pushing Goal Derivation in DLP Computations. In: Gelfond, M., Leone, N., Pfeifer, G. (eds.) LPNMR 1999. LNCS (LNAI), vol. 1730, p. 177. Springer, Heidelberg (1999)
Eiter, T., Gottlob, G.: On the Computational Cost of Disjunctive Logic Programming: Propositional Case. AMAI 15, 289–323 (1995)
Feldmann, R., Monien, B., Schamberger, S.: A Distributed Algorithm to Evaluate Quantified Boolean Formulae. In: Proceedings National Conference on AI (AAAI 2000), Austin, Texas, pp. 285–290. AAAI Press, Menlo Park (2000)
Letz, R.: Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, pp. 160–175. Springer, Heidelberg (2002)
Biere, A.: Resolve and Expand. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 59–70. Springer, Heidelberg (2005)
Zhang, L., Malik, S.: Towards a Symmetric Treatment of Satisfaction and Conflicts in Quantified Boolean Formula Evaluation. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 200–215. Springer, Heidelberg (2002)
Cadoli, M., Eiter, T., Gottlob, G.: Default Logic as a Query Language. IEEE TKDE 9, 448–463 (1997)
Zolda, M.: Comparing Different Prenexing Strategies for Quantified Boolean Formulas. Master’s thesis, TU Wien (2005)
Castellini, C., Giunchiglia, E., Tacchella, A.: SAT-based planning in complex domains: Concurrency, constraints and nondeterminism. Artificial Intelligence 147, 85–117 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Faber, W., Ricca, F. (2005). Solving Hard ASP Programs Efficiently. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2005. Lecture Notes in Computer Science(), vol 3662. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11546207_19
Download citation
DOI: https://doi.org/10.1007/11546207_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28538-0
Online ISBN: 978-3-540-31827-9
eBook Packages: Computer ScienceComputer Science (R0)