Inferring Congruence Equations Using SAT

Authors:
Andy King;Harald Søndergaard
Affiliations:
Portcullis Computer Security Limited, Pinner, UK HA5 2EX;The University of Melbourne, Victoria, Australia 3010
Venue:
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Year:
2008

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Abstract

This paper proposes a new approach for deriving invariants that are systems of congruence equations where the modulo is a power of 2. The technique is an amalgam of SAT-solving, where a propositional formula is used to encode the semantics of a basic block, and abstraction, where the solutions to the formula are systematically combined and summarised as a system of congruence equations. The resulting technique is more precise than existing congruence analyses since a single optimal transfer function is derived for a basic block as a whole.