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Visibly Pushdown Kleene Algebra and Its Use in Interprocedural Analysis of (Mutually) Recursive Programs

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Relations and Kleene Algebra in Computer Science (RelMiCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5827))

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Abstract

Kleene algebra is a great formalism for doing intraprocedural analysis and verification of programs, but it seems difficult to deal with interprocedural analysis where the power of context-free languages is often needed to represent both the program and the property. In the model checking framework, Alur and Madhusudan defined visibly pushdown automata, which accept a subclass of context-free languages called visibly pushdown languages, to do some interprocedural analyses of programs while remaining decidable. We present visibly pushdown Kleene algebra, an extension of Kleene algebra that axiomatises exactly the equational theory of visibly pushdown languages. The algebra is simply Kleene algebra along with a family of implicit least fixed point operators. Some interprocedural analyses of (mutually) recursive programs are possible in this formalism and it can deal with some non-regular properties.

This research is supported by NSERC and FQRNT.

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Authors and Affiliations

  1. Département d’informatique et de génie logiciel, Université Laval, Québec, QC, G1K 7P4, Canada

    Claude Bolduc & Béchir Ktari

Authors
  1. Claude Bolduc
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  2. Béchir Ktari
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Editors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Rudolf Berghammer

  2. College of Engineering, Qatar University, P.O. Box 2713, CSE 209, Doha, Qatar,  

    Ali Mohamed Jaoua

  3. Institut für Informatik, Universität Augsburg, Universitätsstr. 6a, 86135, Augsburg, Germany

    Bernhard Möller

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Bolduc, C., Ktari, B. (2009). Visibly Pushdown Kleene Algebra and Its Use in Interprocedural Analysis of (Mutually) Recursive Programs. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2009. Lecture Notes in Computer Science, vol 5827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04639-1_4

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  • DOI: https://doi.org/10.1007/978-3-642-04639-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04638-4

  • Online ISBN: 978-3-642-04639-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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