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Automata-Based Termination Proofs

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Implementation and Application of Automata (CIAA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5642))

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Abstract

This paper proposes a framework for detecting termination of programs handling infinite and complex data domains, such as pointer structures. In this framework, the user has to specify a finite number of well-founded relations on the data domain manipulated by these programs. Our tool then builds an initial abstraction of the program, which is checked for existence of potential infinite runs, by testing emptiness of its intersection with a predefined Büchi automaton. If the intersection is non-empty, a lasso-shaped counterexample is found. This counterexample is checked for spuriousness by a domain-specific procedure, and in case it is found to be spurious, the abstraction is refined, again by intersection with the complement of the Büchi automaton representing the lasso. We have instantiated the framework for programs handling tree-like data structures, which allowed us to prove termination of programs such as the depth-first tree traversal, the Deutsch-Schorr-Waite tree traversal, or the linking leaves algorithm.

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Author information

Authors and Affiliations

  1. VERIMAG, CNRS, 2 av. de Vignate, F-38610, Gières

    Radu Iosif

  2. FIT, BUT, Božetěchova 2, CZ-61266, Brno

    Adam Rogalewicz

Authors
  1. Radu Iosif
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  2. Adam Rogalewicz
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Editor information

Editors and Affiliations

  1. NICTA and University of New South Wales, Sydney, Australia

    Sebastian Maneth

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© 2009 Springer-Verlag Berlin Heidelberg

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Iosif, R., Rogalewicz, A. (2009). Automata-Based Termination Proofs. In: Maneth, S. (eds) Implementation and Application of Automata. CIAA 2009. Lecture Notes in Computer Science, vol 5642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02979-0_20

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  • DOI: https://doi.org/10.1007/978-3-642-02979-0_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02978-3

  • Online ISBN: 978-3-642-02979-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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