Path invariants

The success of software verification depends on the ability to find a suitable abstraction of a program automatically. We propose a method for automated abstraction refinement which overcomes some limitations of current predicate discovery schemes. In cur-rent schemes, the cause of a false alarm is identified as an infeasi-ble error path, and the abstraction is refined in order to remove that path. By contrast, we view the cause of a false alarm —the spurious counterexample — as a full-fledged program, namely, a fragment of the original program whose control-flow graph may contain loops and represent unbounded computations. There are two advantages to using such path programs as counterexamples for abstraction refinement. First, we can bring the whole machinery of program analysis to bear on path programs, which are typically small com-pared to the original program. Specifically, we use constraint-based invariant generation to automatically infer invariants of path pro-grams —so-called path invariants. Second, we use path invariants for abstraction refinement in order to remove not one infeasibility at a time, but at once all (possibly infinitely many) infeasible er-ror computations that are represented by a path program. Unlike previous predicate discovery schemes, our method handles loops without unrolling them; it infers abstractions that involve universal quantification and naturally incorporates disjunctive reasoning