On Solving Exactly-One-SAT

Abstract

In this paper, we aim at studying the Exactly-One-SAT problem (in short EO-SAT). This problem consists in deciding whether a given CNF formula admits a model so that each clause has exactly one satisfied literal. The contribution of this work is twofold. Firstly, we introduce a tractable class in EO-SAT, which is defined by a property that has to be satisfied by combinations of clauses. This class can be seen as a counterpart of tractable classes in the maximum independent set problem. Secondly, we propose graph-based approaches for reducing the number of variables and clauses of EO-SAT instances, which consequently allow for reducing the search space. We provide an experimental study for evaluating these approach by showing its interest in the context of the graph coloring problem.