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Compositional SCC Analysis for Language Emptiness

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Abstract

We propose a refinement approach to language emptiness, which is based on the enumeration and the successive refinements of SCCs on over-approximations of the exact system. Our algorithm is compositional: It performs as much computation as possible on the abstract systems, and prunes uninteresting part of the search space as early as possible. It decomposes the state space disjunctively so that each state subset can be checked in isolation to decide language emptiness for the given system. We prove that the strength of an SCC or a set of SCCs decreases monotonically with composition. This allows us to deploy the proper model checking algorithms according to the strength of the SCC at hand. We also propose to use the approximate distance of a fair cycle from the initial states to guide the search. Experimental studies on a set of LTL model checking problems prove the effectiveness of our method.

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Authors and Affiliations

  1. NEC Laboratories America, 4 Independence Way, Suite 200, Princeton, NJ, 08540, USA

    Chao Wang

  2. Graz University of Technology, Austria

    Roderick Bloem

  3. University of Colorado, Boulder, USA

    Gary D. Hachtel & Fabio Somenzi

  4. Cadence Design Systems, USA

    Kavita Ravi

Authors
  1. Chao Wang
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  2. Roderick Bloem
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  3. Gary D. Hachtel
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  4. Kavita Ravi
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  5. Fabio Somenzi
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Corresponding author

Correspondence to Chao Wang.

Additional information

This work was done when the first two authors were in University of Colorado at Boulder. Parts of this work appeared in preliminary form in [38] and [39].

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Wang, C., Bloem, R., Hachtel, G.D. et al. Compositional SCC Analysis for Language Emptiness. Form Method Syst Des 28, 5–36 (2006). https://doi.org/10.1007/s10703-006-4617-3

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