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Generalized Model Checking: Reasoning about Partial State Spaces

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CONCUR 2000 — Concurrency Theory (CONCUR 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1877))

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Abstract

We discuss the problem of model checking temporal properties on partial Kripke structures, which were used in [BG99] to represent incomplete state spaces. We first extend the results of [BG99] by showing that the model-checking problem for any 3-valued temporal logic can be reduced to two model-checking problems for the corresponding 2-valued temporal logic. We then introduce a new semantics for 3-valued temporal logics that can give more definite answers than the previous one. With this semantics, the evaluation of a formula φ on a partial Kripke structure M returns the third truth value ⊥ (read “unknown”) only if there exist Kripke structures M 1 and M 2 that both complete M and such that M 1 satisfies φ while M 2 violates φ, hence making the value of φ on M truly unknown. The partial Kripke structure M can thus be viewed as a partial solution to the satisfiability problem which reduces the solution space to complete Kripke structures that are more complete than M with respect to a completeness preorder. This generalized model-checking problem is thus a generalization of both satisfiability (all Kripke structures are potential solutions) and model checking (a single Kripke structure needs to be checked). We present algorithms and complexity bounds for the generalized model-checking problem for various temporal logics.

This is an extended abstract, with proofs omitted. For the full version of the paper see www.bell-labs.com/~grb,god

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Author information

Authors and Affiliations

  1. Bell Laboratories, Lucent Technologies, 263 Shuman Boulevard, Naperville, IL, 60566, USA

    Glenn Bruns & Patrice Godefroid

Authors
  1. Glenn Bruns
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  2. Patrice Godefroid
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Pennsylvania State University, 220 Pond Laboratory, University Park, PA, 16802-6106, USA

    Catuscia Palamidessi

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Bruns, G., Godefroid, P. (2000). Generalized Model Checking: Reasoning about Partial State Spaces. In: Palamidessi, C. (eds) CONCUR 2000 — Concurrency Theory. CONCUR 2000. Lecture Notes in Computer Science, vol 1877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44618-4_14

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  • DOI: https://doi.org/10.1007/3-540-44618-4_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67897-7

  • Online ISBN: 978-3-540-44618-7

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