Solving Not-Substring Constraint with Flat Abstraction

Not-substring is currently among the least supported types of string constraints, and existing solvers use only relatively crude heuristics. Yet, not-substring occurs relatively often in practical examples and is useful in encoding other types of constraints. In this paper, we propose a systematic way to solve not-substring using the Counter-Example Guided Abstraction Refinement (CEGAR) framework based on flat abstraction. In such a framework, the domain of string variables is restricted to flat languages and subsequently, the whole constraints can be expressed as linear arithmetic formulae. We show that non-substring constraints can be flattened efficiently, and provide experimental evidence that the proposed solution for not-substring is competitive with the state-of-the-art string solvers.