Linear absolute value relation analysis

Authors:
Liqian Chen;Antoine Miné;Ji Wang;Patrick Cousot
Affiliations:
National Laboratory for Parallel and Distributed Processing, Changsha, P.R. China;École Normale Supérieure, Paris, France and CNRS, France;National Laboratory for Parallel and Distributed Processing, Changsha, P.R. China;École Normale Supérieure, Paris, France and CIMS, New York University, New York, NY
Venue:
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
Year:
2011

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Abstract

Linear relation analysis (polyhedral analysis), devoted to discovering linear invariant relations among variables of a program, remains one of the most powerful abstract interpretations but is subject to convexity limitations. Absolute value enjoys piecewise linear expressiveness and thus natively fits to encode certain non-convex properties. Based on this insight, we propose to use linear absolute value relation analysis to discover linear relations among values and absolute values of program variables. Under the framework of abstract interpretation, the analysis yields a new numerical abstract domain, namely the abstract domain of linear absolute value inequalities (Σkakxk + Σkbk|xk| ≤ c), which can be used to analyze programs involving piecewise linear behaviors (e.g., due to conditional branches or absolute value function calls). Experimental results of our prototype are encouraging; The new abstract domain can find non-convex invariants of interest in practice.