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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)

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)

Let F be a conjunction of atoms of the form max(x, y)+k ≥ z, where x, y, z are variables and k is a constant value. Here we consider the satisfiability problem of such formulas (e.g., over the integers or ra-tionals). This problem, which appears in unexpected forms in many applications , is easily shown to be in NP. However, decades of efforts (in several… (More)

Predicate abstraction is a technique for automatically extracting finite-state abstractions for systems with potentially infinite state space. The fundamental operation in predicate abstraction is to compute the best approximation of a Boolean formula ϕ over a set of predicates P. In this work, we demonstrate the use for this operation of a decision… (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)