Design and Implementation of Satisfiability Solver of Formulas about Strings

Abstract

We developed a solver of the satisfiability problems of quantifier free first order formulas containing stringrelated functions and predicates. In this paper, we describe the design and the implementation of the solver. Our method is based on Makanin/Jaffar's word unification algorithm, but is extended to be able to handle constraints of assignable lengths of variables and possible occurrence counts of letters in the variables. To implement this, we propose a hooking calculation method (HC method) to combine a word unification solver and a QFP solver. The soundness of the combination is kept by ‘basic relation’ of strings and their attributes. Jaffar's algorithm is known to be complicated, but we show our solver can solve relatively small-sized problems, which usually appear in software verification situations, in practical time.