Abstract
Quantified Boolean formulas (QBFs) play an important role in artificial intelligence subjects, specially in planning, knowledge representation and reasoning [20]. In this paper we present ZQSAT (sibling of our FZQSAT [15]), which is an algorithm for evaluating quantified Boolean formulas. QBF is a language that extends propositional logic in such a way that many advanced forms of reasoning can be easily formulated and evaluated. ZQSAT is based on ZDD, which is a variant of BDD, and an adopted version of the DPLL algorithm. The program has been implemented in C using the CUDD package. The capability of ZDDs in storing sets of subsets efficiently enabled us to store the clauses of a QBF very compactly and led us to implement the search algorithm in such a way that we could store and reuse the results of all previously solved subformulas with few overheads. This idea along some other techniques, enabled ZQSAT to solve some standard QBF benchmark problems faster than the best existing QSAT solvers.
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References
Achröer, O., Wegener, I.: The Theory of Zero-Suppressed BDDs and the Number of Knight’s Tours. Formal Methods in System Design 13(3) (November 1998)
Aloul, F.A., Mneimneh, M.N., Sakallah, K.A.: ZBDD-Based Backtrack Search SAT Solver. In: International Workshop on Logic and Synthesis (IWLS), New Orleans, Louisiana, pp. 131–136 (2002)
www.bdd-portal.org. http://www.bdd-portal.org
Bern, J., Meinel, C., Slobodová, A.: OBDD-Based Boolean manipulation in CAD beyound current limits. In: Proceedings 32nd ACM/IEEE Design Automation Conference, San Francisco, CA, pp. 408–413 (1995)
Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers 35, 677–691 (1986)
Bryant, R.E., Meinel, C.: Ordererd Binary Decision Diagrams in Electronic Design Automation chapter 11. Kluwer Academic Publishers, Dordrecht (2002)
Cadoli, M., Schaerf, M., Giovanardi, A., Giovanardi, M.: An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation. Journal of Automated Reasoning 28(2), 101–142 (2002)
Chatalic, P., Simon, L.: Multi-Resolution on Compressed Sets of Cluases. In: Proceedings of the 12th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2000 (2000)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Communication of the ACM 5, 394–397 (1962)
Sakallah, K.A., Aloul, F.A., Mneimneh, M.N.: Backtrack Search Using ZBDDs. In: International Workshop on Logic and Synthesis (IWLS), June 2001, p. 5. University of Michigan (2001)
Feldmann, R., Monien, B., Schamberger, S.: A Distributed Algorithm to Evaluate Quantified Boolean Formulae. In: Proceedings of the 17th National Conference on Artificial Intelligence, AAAI-2000 (2000)
Giunchiglia, E., Narizzano, M., Tacchella, A.: QUBE: A System for Deciding Quantified Boolean Formulas Satisfiability. In: Proceedings of the International Joint Conference on Automated Reasoning, pp. 364–369 (2001)
Letz, R.: Efficient Decision Procedures for Quantified Boolean Formulas. Vorlesung WS 2002/2003 TU Muenchen: Logikbasierte Entscheidungsverfahren
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)
Meinel, C., GhasemZadeh, M., Klotz, V.: FZQSAT: A QSAT Solver for QBFs in Prenex NNF (A Useful Tool for Circuit Verification). In: International Workshop on Logic and Synthesis (IWLS), California, USA, June, pp. 135–142 (2004)
Meinel, C., Theobald, T.: Algorithms and Data Structures in VLSI Design. Springer, Heidelberg (1998)
Minato, S.: Zero-suppressed BDDs for set Manipulation in Combinatorial Problems. In: proceedings of the 30th ACM/IEEE Design Automation Conference (1993)
Mishchenko, A.: An Introduction to Zero-Suppressed Binary Decision Diagrams (June 2001), http://www.ee.pdx.edu/alanmi/research/dd/zddtut.pdf
QBFLIB - Quantified Boolean Formulas Satisfiability Library, http://www.mrg.dist.unige.it/qube/qbflib/
Rintanen, J.: Improvements to the Evaluation of Quantified Boolean Formulae. In: Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI 1999), pp. 1192–1197 (1999)
Wegener, I.: Branching Programs and Binary Decision Diagrams – Theory and Applications. In: SIAM Monographs on Discrete Mathematics and Applications (2000)
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GhasemZadeh, M., Klotz, V., Meinel, C. (2004). Embedding Memoization to the Semantic Tree Search for Deciding QBFs. In: Webb, G.I., Yu, X. (eds) AI 2004: Advances in Artificial Intelligence. AI 2004. Lecture Notes in Computer Science(), vol 3339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30549-1_59
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DOI: https://doi.org/10.1007/978-3-540-30549-1_59
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