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Applications of Craig Interpolation to Model Checking

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Applications and Theory of Petri Nets 2005 (ICATPN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3536))

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Abstract

A Craig interpolant [1] for a mutually inconsistent pair of formulas (A,B) is a formula that is (1) implied by A, (2) inconsistent with B, and (3) expressed over the common variables of A and B. It is known that a Craig interpolant can be efficiently derived from a refutation of A ∧ B, for certain theories and proof systems. For example, interpolants can be derived from resolution proofs in propositional logic, and for systems of linear inequalities over the reals [6,4]. These methods have been recently extended to combine linear inequalities with uninterpreted function symbols, and to deal with integer models [5]. One key aspect of these procedures is that the yield quantifier-free interpolants when the premises A and B are quantifier-free.

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References

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Authors and Affiliations

  1. Cadence Berkeley Labs,  

    Kenneth McMillan

Authors
  1. Kenneth McMillan
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Editors and Affiliations

  1. UC Riverside,  

    Gianfranco Ciardo

  2. IRISA, CNRS & INRIA, Rennes, France

    Philippe Darondeau

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McMillan, K. (2005). Applications of Craig Interpolation to Model Checking. In: Ciardo, G., Darondeau, P. (eds) Applications and Theory of Petri Nets 2005. ICATPN 2005. Lecture Notes in Computer Science, vol 3536. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494744_2

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  • DOI: https://doi.org/10.1007/11494744_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26301-2

  • Online ISBN: 978-3-540-31559-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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