Counterexample-guided abstraction re\ufb01nement (CEGAR) is a powerful technique to scale automatic program analysis techniques to large programs. However, so far it has been used primarily for model checking in the context of predicate abstraction. We formalize CEGAR for general powerset domains. If a spurious abstract counterexample needs to be removed through abstraction re\ufb01nement, there are often several choices, such as which program location(s) to re\ufb01ne, which abstract domain(s) to use at di\ufb00erent locations, and which abstract values to compute. We de\ufb01ne several plausible preference orderings on abstraction re\ufb01nements, such as re\ufb01ning as \u201clate\u201d as possible and as \u201ccoarse\u201d as possible. We present generic algorithms for \ufb01nding re\ufb01nements that are optimal with respect to the di\ufb00erent preference orderings. We also compare the di\ufb00erent orderings with respect to desirable properties, including the property if locally optimal re\ufb01nements compose to a global optimum. Finally, we point out some di\ufb03culties with CEGAR for nonpowerset domains.<\/p>\n","protected":false},"excerpt":{"rendered":"
Counterexample-guided abstraction re\ufb01nement (CEGAR) is a powerful technique to scale automatic program analysis techniques to large programs. However, so far it has been used primarily for model checking in the context of predicate abstraction. We formalize CEGAR for general powerset domains. 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