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We first introduce <i>Abstract DPLL</i>, 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,(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)
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)
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)
This paper describes our work on applying novel techniques based on propo-sitional satisfiability (SAT) solvers and optimizers to the Curriculum-based Course Time-tabling problem. Out of 32 standard benchmark instances derived from the Second International Time-tabling Competition held in 2007, our techniques yield the best known solutions for 21 of them(More)