### Constraint-based Invariant Inference over Predicate Abstraction

### Abstract

This paper describes a constraint-based invariant generation technique for proving the validity of safety assertions over the domain of predicate abstraction in an interprocedural setting. The key idea of the technique is to represent each invariant in bounded DNF form by means of boolean indicator variables, one for each predicate p and each disjunct d denoting whether p is present in d or not. The verification condition of the program is then encoded by means of a boolean formula over these boolean indicator variables such that any satisfying assignment to the formula yields the inductive invariants for proving the validity of given program assertions.

This paper also describes how to use the constraint-based methodology for generating weakest preconditions for safety assertions. An interesting application of weakest precondition generation is to produce most-general counterexamples for safety assertions. We also present preliminary experimental evidence demonstrating the feasibility of this technique.