Abstract domains of affine relations

Authors:
Matt Elder;Junghee Lim;Tushar Sharma;Tycho Andersen;Thomas Reps
Affiliations:
University of Wisconsin, Madison, WI;University of Wisconsin, Madison, WI;University of Wisconsin, Madison, WI;University of Wisconsin, Madison, WI;University of Wisconsin, Madison, WI and GrammaTech, Inc., Ithaca, NY
Venue:
SAS'11 Proceedings of the 18th international conference on Static analysis
Year:
2011

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Abstract

This paper considers some known abstract domains for affine-relation analysis (ARA), along with several variants, and studies how they relate to each other. We show that the abstract domains of Müller-Olm/Seidl (MOS) and King/Søndergaard (KS) are, in general, incomparable, but give sound interconversion methods. We also show that the methods of King and Søndergaard can be applied without bit-blasting--while still using a bit-precise concrete semantics.