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

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**ABSTRACT:**Knowledge compilation is a process of adding more information to a knowledge base in order to make it easier to deduce facts from the compiled base than from the original one. One type of knowledge compilation occurs when the knowledge in question is represented by a Boolean formula in conjunctive normal form (CNF). The goal of knowledge compilation in this case is to add clauses to the input CNF until a logically equivalent propagation complete CNF is obtained. A CNF is called propagation complete if after any partial substitution of truth values all logically entailed literals can be inferred from the resulting CNF formula by unit propagation. The key to this type of knowledge compilation is the ability to generate so-called empowering clauses. A clause is empowering for a CNF if it is an implicate and for some partial substitution of truth values it enlarges the set of entailed literals inferable by unit propagation. In this paper we study several complexity issues related to empowering implicates, propagation completeness, and its relation to resolution proofs. We show several results: (a) given a CNF and a clause it is co-NP complete to decide whether the clause is an empowering implicate of the CNF, (b) given a CNF it is NP-complete to decide whether there exists an empowering implicate for it and thus it is co-NP complete to decide whether a CNF is propagation complete, and (c) there exist CNFs to which an exponential number of clauses must be added to make them propagation complete.Artificial Intelligence. 01/2013; 203:19–34. - [Show abstract] [Hide abstract]

**ABSTRACT:**The propositional satisfiability SAT problem is one of the most fundamental problems in computer science. SAT solvers have been successfully applied to a wide range of practical applications, including hardware model checking, software model finding, equivalence checking, and planning, among many others. Empirical research has been very fruitful for the development of efficient methods for SAT problems, such as classical Davis-Putnam method, greedy SAT GSAT method and neural network SAT method. This paper gives a survey about the methods used for solving the SAT problems with an emphasis on surveying the local search algorithms.International Journal of Advanced Intelligence Paradigms 09/2013; 5(3):233-256. - [Show abstract] [Hide abstract]

**ABSTRACT:**We offer a new understanding of some aspects of practical SAT-solvers that are based on DPLL with unit-clause propagation, clause-learning, and restarts. We do so by analyzing a concrete algorithm which we claim is faithful to what practical solvers do. In particular, before making any new decision or restart, the solver repeatedly applies the unit-resolution rule until saturation, and leaves no component to the mercy of non-determinism except for some internal randomness. We prove the perhaps surprising fact that, although the solver is not explicitly designed for it, with high probability it ends up behaving as width-k resolution after no more than O(n^2k+2) conflicts and restarts, where n is the number of variables. In other words, width-k resolution can be thought of as O(n^2k+2) restarts of the unit-resolution rule with learning.Journal of Artificial Intelligence Research 01/2014; 40. · 1.06 Impact Factor

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