Conference Paper

A New Clause Learning Scheme for Efficient Unsatisfiability Proofs.

Conference: Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, Chicago, Illinois, USA, July 13-17, 2008
Source: DBLP


We formalize in this paper a key property of asserting clauses (the most common type of clauses learned by SAT solvers). We show that the formalized property, which is called em- powerment, is not exclusive to asserting clauses, and intro- duce a new class of learned clauses which can also be empow- ering. We show empirically that (1) the new class of clauses tends to be much shorter and induce further backtracks than asserting clauses and (2) an empowering subset of this new class of clauses significantly improves the performance of the Rsat solver on unsatisfiable problems.


Available from: Thammanit Pipatsrisawat, Jul 15, 2014
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    • "SAT has also been extended to a variety of applications in Artificial Intelligence including other well-known NP-complete problems such as graph colorability, vertex cover, hamiltonian path, and independent sets [12]. Despite SAT being an NP-Complete problem [13], many researchers have developed powerful SAT solvers that are able of handling problems consisting of thousands of variables and millions of constraints [14] [15] [16] [17] [18] [19] [20] [21] [22]. Briefly defined, the SAT problem involves a set of Boolean variables and a set of constraints expressed in product-of-sum form. "
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    ABSTRACT: A new technique for multipath detection in wideband mobile radio systems is presented. The proposed scheme is based on an intelligent search algorithm using Boolean Satisfiability (SAT) techniques to search through the uncertainty region of the multipath delays. The SAT-based scheme utilizes the known structure of the transmitted wideband signal, for example, pseudo-random (PN) code, to effectively search through the entire space by eliminating subspaces that do not contain a possible solution. The paper presents a framework for modeling the multipath detection problem as a SAT application. It also provides simulation results that demonstrate the effectiveness of the proposed scheme in detecting the multipath components in frequency-selective Rayleigh fading channels.
    Journal of Computer Systems Networks and Communications 01/2011; 2011. DOI:10.1155/2011/365107
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    • "Modern SAT solvers use some sophisticated data structures, implement clause learning [20], [21], perform non-chronological backtrack [20], [22] and restarts [23], [24], [25]. It is shown that clause learning is a powerful notion [26], [27], [28], [29] that improves dramatically the efficiency of solvers. Symmetry had been shown to be useful for SAT solvers but never used in clause learning. "
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    ABSTRACT: The satisfiability problem (SAT) is shown to be the first decision NP-complete problem. It is central in complexity theory. A CNF formula usually contains an interesting number of symmetries. That is, the formula remains invariant under some variable permutations. Such permutations are the symmetries of the formula, their elimination can lead to make a short proof for a satisfiability proof procedure. On other hand, many improvements had been done in SAT solving, Conflict-Driven Clause Learning (CDCL) SAT solvers are now able to solve great size and industrial SAT instances efficiently. The main theoretical key behind these modern solvers is, they use lazy data structures, a restart policy and perform clause learning at each fail end point in the search tree. Although symmetry and clause learning are shown to be powerful principles for SAT solving, but their combination, as far as we now, is not investigated. In this paper, we will show how symmetry can be used to improve clause learning in CDCL SAT solvers. We implemented the symmetry clause learning approach on the MiniSat solver and experimented it on several SAT instances. We compared both MiniSat with and without symmetry and the results obtained are very promising and show that clause learning by symmetry is profitable for CDCL SAT solvers.
    Tools with Artificial Intelligence (ICTAI), 2010 22nd IEEE International Conference on; 11/2010
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    • "Ces derniers utilisent de meilleures structures de données, l'apprentissage de clauses [29] [31], le retour arrière non chronologique [29] [21] et différentes politiques de redémarrage [18] [20] [3]. Il a été montré que l'apprentissage est une notion importante [5] [19] [24] [25] qui améliore grandement lâefficacité des solveurs. L'utilisation des symétries est tout aussi utile pour les solveurs SAT mais n'a jamais été utilisée dans l'apprentissage de clauses. "
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    ABSTRACT: Le problème de satisfiabilité (SAT) est le premier problème de décision à avoir été montré NP-complet. Il est central en théorie de la complexité. Une for- mule mise sous forme CNF contient un nombre inté- ressant de symétries. En d'autres termes, la formule reste invariante si l'on permute quelques variables. De telles permutations sont les symétries de la formule et leurs éliminations peuvent conduire à une preuve plus courte pour la satisfiabilité. D'autre part, de nom- breuses améliorations ont été apportées dans les sol- veurs actuels. Les solveurs de type CDCL sont aujour- d'hui capables de résoudre de manière efficace des problèmes industriels de très grande taille (en nombre de variables et de clauses). Ces derniers utilisent des structures de données paresseuses, des politiques de redémarrage et apprennent de nouvelles clauses à chaque échec au cours de la recherche. Bien que l'uti- lisation des symétries et l'apprentissage de clauses s'avèrent être des principes puissants, la combinai- son des deux n'a encore jamais été exploitée. Dans cet article, nous allons montrer comment la symétrie peut être utilisée afin d'améliorer l'apprentissage dans des solveurs de type CDCL. Nous avons mis en ap- plication l'apprentissage par symétries dans MiniSat et nous l'avons expérimenté sur différents problèmes. Nous avons comparé MiniSat avec et sans apprentis- sage par symétries. Les résultats obtenus sont très en- courageants et montrent que l'utilisation des symétries dans l'apprentissage est profitable pour des solveurs à base de CDCL.
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