Multi-valued Problem Solvers

Abstract

Many problems can be described by the question: Is there an assignment of values to given variables that satisfies certain conditions? Such problems are called satisfiability problems (SAT-problems). The values of the variables are usually encodedby Boolean values, and the conditions are transformed into a single expression consisting of conjunctions (C) of disjunctions(D) of Boolean variables. Due to this structure of the Boolean expression these satisfiability problems are more precisely calledCD-SAT-problems. Due to the wide field of applications and the simple unique representation, universal SAT-solvers were developed and stronglyimproved over the decades [2]. It is possible to solve CDSAT-problems of a few hundred Boolean variables and severalthousand disjunctions. The necessary Boolean encoding of binary variables restricts the application of CD-SAT-solvers for multivalued problems to a relatively small number of multi-valued variables and a small size of their domains. Therefore, wedeveloped a multi-valued problem solver that allows the solution for conjunctions (C) of disjunctions (D) of multi-valued variablesin the expression to be solved, we call it MV-CD-SAT-solver. A drawback of the required specification of a CD-SAT-problemis the distribution of knowledge about the problem over a large number of disjunctions (clauses). Some problems to be solved canbe specified more compactly by a conjunction (C) of disjunctions (D) of conjunctions (C). We utilized this possibility in an MVCDC-SAT-solver. Our experimental results confirm the benefits of this approach for the solution of multi-valued problems.