Lionel Paris

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In this paper, a new approach for computing strong backdoor sets of Boolean formula in conjunctive normal form (CNF) is proposed. It makes an original use of local search techniques for finding an assignment leading to a largest renamable Horn sub-formula of a given CNF. More precisely, at each step, preference is given to variables such that when assigned(More)
The main purpose of the paper is to solve structured instances of the satisfiability problem. The structure of a SAT instance is represented by an hypergraph, whose vertices correspond to the variables and the hyper-edges to the clauses. The proposed method is based on a tree decomposition of this hyper-graph which guides the enumeration process of a(More)
Given a Boolean formula in conjunctive normal form (CNF), the exact satisfiability problem (XSAT), a variant of the satisfiability problem (SAT), consists in finding an assignment to the variables such that each clause contains exactly one satisfied literal. Best algorithms to solve this problem runs in O(2<sup>0.2325n</sup>) (O(2<sup>0.1379n</sup>) for(More)
We investigate in this work a generalization of the known CNF representation that we call General Normal Form (GNF) and extend the resolution rule of Robinson to design a new sound and complete resolution proof system for the GNF. We show that by using a cardinality operator in the GNF we obtain the new representation CGNF that allows a natural and(More)
In 1997, B. Selman and H. Kautz proposed a series of 10 challenges. One of them concerned the design of a practical stochastic local search procedure for proving unsatisfiability (Challenge 5). Today, more than 10 years later, only few attempts were led to address this challenge, in spite of the great number of incomplete methods for proving satisfiability.(More)
In this paper, we propose a new approach for solving the SAT problem. This approach consists in representing SAT instances thanks to an undirected graph issued from a polynomial transformation from SAT to the CLIQUE problem. Considering this graph, we exploit well known properties of chordal graphs to manipulate the SAT instance. Firstly, these properties(More)
Identifying and exploiting hidden problem structures is recognized as a fundamental way to deal with the intractability of combina-torial problems. Recently, a particular structure called (strong) backdoor has been identified in the context of the satisfiability problem. Connections has been established between backdoors and problem hardness leading to a(More)
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