Predicate abstraction with indexed predicates

Authors:
Shuvendu K. Lahiri;Randal E. Bryant
Affiliations:
Carnegie Mellon University, Pittsburgh, PA;Carnegie Mellon University, Pittsburgh, PA
Venue:
ACM Transactions on Computational Logic (TOCL)
Year:
2007

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Abstract

Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model checking. We consider models containing first-order state variables, where the system state includes mutable functions and predicates. Such a model can describe systems containing arbitrarily large memories, buffers, and arrays of identical processes. We describe a form of predicate abstraction that constructs a formula over a set of universally quantified variables to describe invariant properties of the first-order state variables. We provide a formal justification of the soundness of our approach and describe how it has been used to verify several hardware and software designs, including a directory-based cache coherence protocol.