Bridging the Gap between SAT and CSP

Abstract

Our research program is aimed at bridging the gap between propositional satisfiability encodings and constraint satisfaction formalisms. The challenge is to combine the inherent efficiencies of SAT solvers operating on uniform satisfiability encodings with the much more compact and natural representations, and more sophisticated propagation techniques of CSP formalisms. Our research objective is to define a new language —MV-SAT— that incorporates the best characteristics of the existing many-valued languages [1,2], as well as to develop fast MV-SAT solvers. MV-SAT is formally defined as the problem of deciding the satisfiability of MV-formulas. An MV-formula is a classical propositional conjunctive clause form based on a generalized notion of literal, called MV-literal. Given a domain T (|T| ≥ 2) equipped with a total ordering ≤, an MV-literal is an expression of the form S: p, where p is a propositional variable and S is a subset of T which is of the form {i}, ↑ i = {j ∈ T | j ≥ i}, or ↓ i = {j ∈ T | j ≤ i} for some i ∈ T. The informal meaning of S: p is “p is constrained to the values in S”.

Research partially supported by the project CICYT TIC2001-1577-C03-03.