Generation of Basic Semi-algebraic Invariants Using Convex Polyhedra

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Generation of Basic Semi-algebraic Invariants Using Convex Polyhedra
A technique for generating invariant polynomial inequalities of bounded degree is presented using the abstract interpretation framework. It is based on overapproximating basic semi-algebraic sets, i.e., sets defined by conjunctions of polynomial inequalities, by means of convex polyhedra. While improving on the existing methods for generating invariant polynomial equalities, since polynomial inequalities are allowed in the guards of the transition system, the approach does not suffer from the prohibitive complexity of the methods based on quantifier-elimination. The application of our implementation to benchmark programs shows that the method produces non-trivial invariants in reasonable time. In some cases the generated invariants are essential to verify safety properties that cannot be proved with classical linear invariants.
Roberto Bagnara, Enric Rodríguez-Carbonell,
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where SAS
Authors Roberto Bagnara, Enric Rodríguez-Carbonell, Enea Zaffanella
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