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International Static Analysis Symposium

SAS 2010: Static Analysis pp 117–133Cite as

Multi-dimensional Rankings, Program Termination, and Complexity Bounds of Flowchart Programs

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6337))

Abstract

Proving the termination of a flowchart program can be done by exhibiting a ranking function, i.e., a function from the program states to a well-founded set, which strictly decreases at each program step. A standard method to automatically generate such a function is to compute invariants for each program point and to search for a ranking in a restricted class of functions that can be handled with linear programming techniques. Previous algorithms based on affine rankings either are applicable only to simple loops (i.e., single-node flowcharts) and rely on enumeration, or are not complete in the sense that they are not guaranteed to find a ranking in the class of functions they consider, if one exists. Our first contribution is to propose an efficient algorithm to compute ranking functions: It can handle flowcharts of arbitrary structure, the class of candidate rankings it explores is larger, and our method, although greedy, is provably complete. Our second contribution is to show how to use the ranking functions we generate to get upper bounds for the computational complexity (number of transitions) of the source program. This estimate is a polynomial, which means that we can handle programs with more than linear complexity. We applied the method on a collection of test cases from the literature. We also show the links and differences with previous techniques based on the insertion of counters.

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Author information

Authors and Affiliations

  1. Compsys team, LIP, UMR 5668 CNRS—ENS Lyon—UCB Lyon—Inria, Lyon, France

    Christophe Alias, Alain Darte & Paul Feautrier

  2. LIFL - UMR CNRS/USTL 8022, INRIA Lille - Nord Europe, 40 avenue Halley, 59650, Villeneuve d’Ascq, France

    Laure Gonnord

Authors
  1. Christophe Alias
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  2. Alain Darte
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  3. Paul Feautrier
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  4. Laure Gonnord
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Editor information

Editors and Affiliations

  1. Départment d’Informatique, École normale supérieure, rue d’Ulm 45, 75230, Paris cedex, France

    Radhia Cousot

  2. ELIAUS-DALI Laboratory, Université de Perpignan Via Domitia, 52, avenue Paul Alduy, 66860, Perpignan cedex, France

    Matthieu Martel

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Alias, C., Darte, A., Feautrier, P., Gonnord, L. (2010). Multi-dimensional Rankings, Program Termination, and Complexity Bounds of Flowchart Programs. In: Cousot, R., Martel, M. (eds) Static Analysis. SAS 2010. Lecture Notes in Computer Science, vol 6337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15769-1_8

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  • DOI: https://doi.org/10.1007/978-3-642-15769-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15768-4

  • Online ISBN: 978-3-642-15769-1

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