Effective bit-width and under-approximation

Abstract

Recently, it has been proposed to use approximation techniques in the context of decision procedures for the quantifier-free theory of fixed-size bit-vectors. We discuss existing and novel variants of under-approximation techniques. Under-approximations produce smaller models and may reduce solving time significantly. We propose a new technique that allows early termination of an under-approximation refinement loop, although the original formula is unsatisfiable. Moreover, we show how over-approximation and under-approximation techniques can be combined. Finally, we evaluate the effectiveness of our approach on array and bit-vector benchmarks of the SMT library. © 2009 Springer-Verlag Berlin Heidelberg.