A Decision Procedure for String Logic with Equations, Regular Membership and Length Constraints

Abstract: In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making state-of-the-art algorithms non-terminating. Our main contribution is to show that the satisfiability problem in a fragment where no string variable occurs more than twice in an equation is decidable. In particular, we propose a semi-decision procedure for arbitrary string formulae with word equations, regular membership and length functions. The essence of our procedure is an algorithm to enumerate an equivalent set of solvable disjuncts for the formula. We further show that the algorithm always terminates for the aforementioned decidable fragment. Finally, we provide a complexity analysis of our decision procedure to prove that it runs, in the worst case, in factorial time.