Abstract Counterexamples for Non-disjunctive Abstractions

Counterexample-guided abstraction refinement (CEGAR) is an important method for tuning abstractions to properties to be verified. The method is commonly used, for example in selecting predicates for predicate abstraction. To date, however, it has been applied primarily to powerset abstractions, which allow one to speak of an abstract transition system and abstract states. Here, we describe a general framework for CEGAR in non-disjunctive abstractions by introducing a generalized notion of abstract counterexample, and methods for computing such counterexamples. We apply this framework to Indexed Predicate Abstraction (IPA), a promising technique for synthesizing quantified inductive invariants of infinite-state systems. In principle, it can be applied to other non-disjunctive abstractions occurring in program analysis