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 ver-tices 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 enumera-tion process of a(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)
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)
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)
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