Ranking function synthesis for bit-vector relations
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- Cook, B., Kroening, D., Rümmer, P. et al. Form Methods Syst Des (2013) 43: 93. doi:10.1007/s10703-013-0186-4
Ranking function synthesis is a key component of modern termination provers for imperative programs. While it is well-known how to generate linear ranking functions for relations over (mathematical) integers or rationals, efficient synthesis of ranking functions for machine-level integers (bit-vectors) is an open problem. This is particularly relevant for the verification of low-level code. We propose several novel algorithms to generate ranking functions for relations over machine integers: a complete method based on a reduction to Presburger arithmetic, and a template-matching approach for predefined classes of ranking functions based on reduction to SAT- and QBF-solving. The utility of our algorithms is demonstrated on examples drawn from Windows device drivers.