Cesare Tinelli's Publications

Robert Nieuwenhuis, Albert Oliveras, and Cesare Tinelli. Solving SAT and SAT Modulo Theories: from an Abstract Davis-Putnam-Logemann-Loveland Procedure to DPLL(T). Journal of the ACM, 53(6):937-977, November 2006.

Abstract. 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 carry over to the modern DPLL implementations with features such as backjumping or clause learning.
We then extend the framework to Satisfiability Modulo background Theories (SMT) and use it to model several variants of the so-called lazy approach for SMT. In particular, we use it to introduce a few variants of a new, efficient and modular approach for SMT based on 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 DPLL(T) system. We describe the high level design of DPLL(X) and its cooperation with Solver_T, discuss the role of theory propagation, and show how to implement DPLL(T) for some theories arising in industrial applications.
Our extensive experimental evidence, summarized in this paper, shows that DPLL(T) systems can significantly outperform the other state-of-the-art tools, frequently even in orders of magnitude, and have better scaling properties.