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- Robert Nieuwenhuis, Albert Oliveras, Cesare Tinelli
- J. ACM
- 2006

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)

- Robert Nieuwenhuis, Albert Oliveras
- CAV
- 2005

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… (More)

- Robert Nieuwenhuis, Albert Rubio
- Handbook of Automated Reasoning
- 2001

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)

- Robert Nieuwenhuis, Albert Oliveras
- SAT
- 2006

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)

- Robert Nieuwenhuis
- Inf. Process. Lett.
- 1993

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)

- Hubert Comon-Lundh, Robert Nieuwenhuis
- Inf. Comput.
- 2000

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)

Lazy algorithms for Satisfiability Modulo Theories (SMT) combine a generic DPLL-based SAT engine with a theory solver for the given theory T that can decide the T -consistency of conjunctions of ground literals. For many theories of interest, theory solvers need to reason by performing internal case splits. Here we argue that it is more convenient to… (More)

- Roberto Javier Asín Achá, Robert Nieuwenhuis, Albert Oliveras, Enric Rodríguez-Carbonell
- Constraints
- 2010

We introduce Cardinality Networks, a new CNF encoding of cardinality constraints. It improves upon the previously existing encodings such as the sorting networks of Eén and Sörensson (JSAT 2:1–26, 2006) in that it requires much less clauses and auxiliary variables, while arc consistency is still preserved: e.g., for a constraint x 1 + ... + x n ≤ k, as… (More)

- Robert Nieuwenhuis, Albert Rubio
- J. Symb. Comput.
- 1995

Deduction methods for rst-order constrained clauses with equality are described within an abstract framework: constraint strategies, consisting of an inference system, a constraint inheritance strategy and redundancy criteria for clauses and inferences. We give simple conditions for such a constraint strategy to be complete (refutationally and in the sense… (More)