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International Conference on Tools and Algorithms for the Construction and Analysis of Systems

TACAS 2014: Tools and Algorithms for the Construction and Analysis of Systems pp 46–61Cite as

IC3 Modulo Theories via Implicit Predicate Abstraction

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8413)

Abstract

We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit (predicate) Abstraction, a technique that expresses abstract transitions without computing explicitly the abstract system and is incremental with respect to the addition of predicates. In this scenario, IC3 operates only at the Boolean level of the abstract state space, discovering inductive clauses over the abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current abstraction allows for a spurious counterexample, it is refined by discovering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search.

The proposed approach has two key advantages. First, unlike current SMT generalizations of IC3, it allows to handle a wide range of background theories without relying on ad-hoc extensions, such as quantifier elimination or theory-specific clause generalization procedures, which might not always be available, and can moreover be inefficient. Second, compared to a direct exploration of the concrete transition system, the use of abstraction gives a significant performance improvement, as our experiments demonstrate.

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Authors and Affiliations

  1. Fondazione Bruno Kessler, Trento, Italy

    Alessandro Cimatti, Alberto Griggio, Sergio Mover & Stefano Tonetta

Authors
  1. Alessandro Cimatti
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  2. Alberto Griggio
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  3. Sergio Mover
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  4. Stefano Tonetta
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Editor information

Editors and Affiliations

  1. RWTH Aachen, Germany

    Erika Ábrahám

  2. Jet Propulsion Laboratory, California Institute of Technology, USA

    Klaus Havelund

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Cimatti, A., Griggio, A., Mover, S., Tonetta, S. (2014). IC3 Modulo Theories via Implicit Predicate Abstraction. In: Ábrahám, E., Havelund, K. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2014. Lecture Notes in Computer Science, vol 8413. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54862-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-54862-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54861-1

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