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

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