Automata-Based Representations for Arithmetic Constraints in Automated Verification

Abstract

In this paper we discuss efficient symbolic representations for infinite-state systems specified using linear arithmetic constraints. We give new algorithms for constructing finite automata which represent integer sets that satisfy linear constraints. These automata can represent either signed or unsigned integers and have a lower number of states compared to other similar approaches. We experimentally compare different symbolic representations by using them to verify non-trivial specification examples. In many cases symbolic representations based on our construction algorithms outperform the polyhedral representation used in Omega Library, or the automata representation used in LASH.KeywordsSymbolic RepresentationBoolean VariableConstruction AlgorithmAutomaton RepresentationArithmetic FormulaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.