DPLL(T) with Exhaustive Theory Propagation and Its Application to Difference Logic

At CAV’04 we presented the DPLL(T ) approach for satisfiability modulo theories T . It is based on a general DPLL(X) engine whose X can be instantiated with different theory solvers Solver T for conjunctions of literals. Here we go one important step further: we require Solver T to be able to detect all input literals that are T -consequences of the partial model that is being explored by DPLL(X). Although at first sight this may seem too expensive, we show that for difference logic the benefits compensate by far the costs. Here we describe and discuss this new version of DPLL(T ), the DPLL(X) engine, and our Solver T for difference logic. The resulting very simple DPLL(T ) system importantly outperforms the existing techniques for this logic. Moreover, it has very good scaling properties: especially on the larger problems it gives improvements of orders of magnitude w.r.t. the existing state-of-the-art tools.