DPLL(T): Fast Decision Procedures

This work proposes a new approach, namely a general DPLL(X) engine, whose parameter X can be instantiated with a specialized solver Solver T for a given theory T, thus producing a systemDPLL(T).

Abstract

The logic of equality with uninterpreted functions (EUF) and its extensions have been widely applied to processor verification, by means of a large variety of progressively more sophisticated (lazy or eager) translations into propositional SAT. Here we propose a new approach, namely a general DPLL(X) engine, whose parameter X can be instantiated with a specialized solver Solver T for a given theory T, thus producing a system DPLL(T). We describe this DPLL(T) scheme, the interface between DPLL(X) and Solver T , the architecture of DPLL(X), and our solver for EUF, which includes incremental and backtrackable congruence closure algorithms for dealing with the built-in equality and the integer successor and predecessor symbols. Experiments with a first implementation indicate that our technique already outperforms the previous methods on most benchmarks, and scales up very well.