Characterization of the set of models by means of symmetries

Many classes of propositional calculus problems display a large amount of symmetries, i.e. the set of clauses representing such problems remains invariant under certain permutations of variable names. In [2,1] we have shown how such symmetries can be detected and used to simplify satis ability checking. The problem of nding all models of a given CNF propositional theory is known to be hard. More generally, we need to explore a complete proof tree and, in some cases, the set of models is much too large to be represented explicitly. In this paper, we show how symmetries can be used to represent a large set of models by a subset of characteristic models(non symmetric models). The other models can be obtained by applying the computed symmetries. We present an algorithm for enumerating non symmetric models, and we show results obtained on some known problems, such as the pigeon-hole, queens and some other problems derived from mathematical theorems.