On multiple learning schemata in conflict driven solvers

In this preliminary paper we describe a general approach for multiple learning in conflict-driven SAT solvers. The proposed formulation of the conflict analysis task turns out to be expressive enough to reckon with different orthogonal generalizations of the standard learning schemata, such as the conjunct analysis of multiple conflicts, the generation of possibly interdependent learned clauses, the imposition of global optimality criteria. We formalize the general learning problem as a search for a collection of vertex cuts in a directed acyclic graph. Optimality of the solution may be evaluated with respect to a given global objective function intended to encode search strategies and heuristics affecting the behavior of the solver. We also outline some algorithmical solutions by exploiting standard algorithms proposed to solve cut and multicut problems on DAGs.