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We first introduce Abstract DPLL, a rule-based formulation of the Davis-Putnam-Logemann-Loveland (DPLL) procedure for propositional satisfiability. This abstract framework allows one to cleanly express practical DPLL algorithms and to formally reason about them in a simple way. Its properties, such as soundness, completeness or termination, immediately… (More)

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… (More)

In the early 80's, there was a number of papers on what should be called proofs by consistency. They describe how to perform inductive proofs, without using an explicit induction scheme, in the context of equational speciications and ground-convergent rewrite systems. The method was explicitly stated as a rst-order consistency proof in case of pure… (More)

Solvers for SAT Modulo Theories (SMT) can nowadays handle large industrial (e.g., formal hardware and software verification) problems over theories such as the integers, arrays, or equality. Here we show that SMT approaches can also efficiently solve problems that, at first sight, do not have a typical SMT flavor. In particular, here we deal with SAT and… (More)

At CAV'04 we presented the DPLL(T) approach for satis-fiability 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… (More)

We present simple techniques for deciding the satissability of lexicographic path ordering constraints under two diierent semantics: solutions built over the given signature and solutions in extended signatures. For both cases we give the rst NP algorithms, which is optimal as we prove the problems to be NP-complete. We discuss the eecient applicability of… (More)

Many applications of congruence closure nowadays require the ability of recovering, among the thousands of input equations, the small subset that caused the equivalence of a given pair of terms. For this purpose, here we introduce an incremental congruence closure algorithm that has an additional Explain operation. First, two variations of union-find data… (More)