Syntactic program transformations for automatic abstraction

Abstract

We present an algorithm that constructs a finite state “abstract” program from a given, possibly infinite state, “concrete” program by means of a syntactic program transformation. Starting with an initial set of predicates from a specification, the algorithm iteratively computes the predicates required for the abstraction relative to that specification. These predicates are represented by boolean variables in the abstract program. We show that the method is sound, in that the abstract pro- gram is always guaranteed to simulate the original. We also show that the method is complete, in that, if the concrete program has a finite abstraction with respect to simulation (bisimulation) equivalence, the algorithm can produce a finite simulation-equivalent (bisimulation-equivalent) abstract program. Syntactic abstraction has two key advantages: it can be applied to infinite state programs or programs with large data paths, and it permits the effective application of other reduction methods for model checking. We show that our method generalizes several known algorithms for analyzing syntactically restricted, data-insensitive programs.