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Termination Proofs for Linear Simple Loops

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Static Analysis (SAS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7460))

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Abstract

Analysis of termination and other liveness properties of an imperative program can be reduced to termination proof synthesis for simple loops, i.e., loops with only variable updates in the loop body. Among simple loops, the subset of Linear Simple Loops (LSLs) is particular interesting because it is common in practice and expressive in theory. Existing techniques can successfully synthesize a linear ranking function for an LSL if there exists one. However, when a terminating LSL does not have a linear ranking function, these techniques fail. In this paper we describe an automatic method that generates proofs of universal termination for LSLs based on the synthesis of disjunctive ranking relations. The method repeatedly finds linear ranking functions on parts of the state space and checks whether the transitive closure of the transition relation is included in the union of the ranking relations. Our method extends the work of Podelski and Rybalchenko [27]. We have implemented a prototype of the method and have shown experimental evidence of the effectiveness of our method.

This research is partially supported by NSF under the grant 0965024. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Louisiana State University, Baton Rouge, LA, 70803, USA

    Hong Yi Chen & Supratik Mukhopadhyay

  2. Department of Computer Science, The Technion, Haifa, 32000, Israel

    Shaked Flur

Authors
  1. Hong Yi Chen
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  2. Shaked Flur
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  3. Supratik Mukhopadhyay
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Editor information

Editors and Affiliations

  1. Département d’Informatique, École Normale Supérieure, 45, rue d’Ulm, 75005, Paris, France

    Antoine Miné

  2. Department of Computing and Information Sciences, Kansas State University, 234 Nichols Hall, 66506, Manhattan, KS, USA

    David Schmidt

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Chen, H.Y., Flur, S., Mukhopadhyay, S. (2012). Termination Proofs for Linear Simple Loops. In: Miné, A., Schmidt, D. (eds) Static Analysis. SAS 2012. Lecture Notes in Computer Science, vol 7460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33125-1_28

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  • DOI: https://doi.org/10.1007/978-3-642-33125-1_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33124-4

  • Online ISBN: 978-3-642-33125-1

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