In predicate abstraction, exact image computation is problematic, requiring in the worst case an exponential number of calls to a decision procedure. For this reason, software model checkers typically use a weak approximation of the image. This can result in a failure to prove a property, even given an adequate set of predicates. We present an interpolant-based method for strengthening the abstract transition relation in case of such failures. This approach guarantees convergence given an adequate set of predicates, without requiring an exact image computation. We show empirically that the method converges more rapidly than an earlier method based on counterexample analysis.
Predicate abstraction is a useful form of abstraction for the verification of transition systems with large or infinite state spaces. One of the main bottlenecks of this approach is the extremely large number of decision procedures calls that are required to construct the abstract state space. In this paper we propose the use of a symbolic decision procedure and its application for predicate abstraction. The advantage of the approach is that it reduces the number of calls to the decision procedure exponentially and also provides for reducing the re-computations inherent in the current approaches. We provide two implementations of the symbolic decision procedure: one based on BDDs which leverages the current advances in early quantification algorithms, and the other based on SAT-solvers. We also demonstrate our approach with quantified predicates for verifying parameterized systems. We illustrate the effectiveness of this approach on benchmarks from the verification of microprocessors, communication protocols, parameterized systems, and Microsoft Windows device drivers.