Exploiting Sparsity in Difference-Bound Matrices

Graeme Gange, Jorge A. Navas, Peter Schachte, Harald Søndergaard, Peter J. Stuckey

Abstract: Relational numeric abstract domains are very important in program analysis. Common domains, such as Zones and Octagons, are usually conceptualised with weighted digraphs and implemented using difference-bound matrices (DBMs). Unfortunately, though conceptually simple, direct implementations of graph-based domains tend to perform poorly in practice, and are impractical for analyzing large code-bases. We propose new DBM algorithms that exploit sparsity and closed operands. In particular, a new representation which we call split normal form reduces graph density on typical abstract states. We compare the resulting implementation with several existing DBM-based abstract domains, and show that we can substantially reduce the time to perform full DBM analysis, without sacrificing precision.