Generation of basic semi-algebraic invariants using convex polyhedra

Abstract

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 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 just classical linear invariants.