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Decision procedures for SMT problems based on the theory of bit-vectors are afundamental component in state-of-the-art software and hardware verifiers.While very efficient in general, certain SMT instances are still challengingfor state-of-the-art solvers (especially when such instances includecomputationally costly functions). In this work, we present an approach for thequantifier-free bit-vector theory (QF_BV in SMT-LIB) based on incremental SMTsolving and abstraction refinement. We define four concrete approximation stepsfor the multiplication, division and remainder operators and combine them intoan incremental abstraction scheme. We implement this scheme in a prototypeextending the SMT solver Boolector and measure both the overall performance andthe performance of the single approximation steps. The evaluation shows thatour abstraction scheme contributes to solving more unsatisfiable benchmarkinstances, including seven instances with unknown status in SMT-LIB.

An Incremental Abstraction Scheme for Solving Hard SMT-Instances over Bit-Vectors