Exotic Semi-Ring Constraints

Exotic semiring constraints arise in a variety of applications and in particular in the context of automated termination analysis. We propose two techniques to solve such constraints: (a) to model them using Boolean functions and integer linear arithmetic and solve them using an SMT solver (QF LIA, in certain cases also QF IDL); and (b) to seek finite domain solutions by applying unary bit-blasting and solve them using a SAT solver. In this note, we show the structure of such systems of constraints, and report on the performance of SMT solvers and SAT encodings when solving them. In particular, we observe that good results are obtained by unary bit-blasting, improving on previous proposals to apply binary bit-blasting. Moreover, our results indicate that, for our benchmarks, unary bit-blasting leads to better results than the ones directly obtained by an SMT solver.