Loop refinement using octagons and satisfiability

Authors:
Jörg Brauer;Volker Kamin;Stefan Kowalewski;Thomas Noll
Affiliations:
Embedded Software Laboratory, RWTH Aachen University;Embedded Software Laboratory, RWTH Aachen University;Embedded Software Laboratory, RWTH Aachen University;Software Modelling and Verification Group, RWTH Aachen University
Venue:
SSV'10 Proceedings of the 5th international conference on Systems software verification
Year:
2010

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Abstract

This paper presents a technique for refining the control structure of loops in programs operating over finite bit-vectors. This technique is based on abstract interpretation using octagons and affine equalities in order to identify infeasible sequences of loop iterations. Our approach naturally integrates wrap-around arithmetic during the generation of abstractions. Abstract interpreters operating on a refined control structure then typically derive strengthened program invariants without having to rely on complicated domain constructions such as disjunctive completions.