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On the Termination of Integer Loops

  • Conference paper
Verification, Model Checking, and Abstract Interpretation (VMCAI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7148))

Abstract

In this paper we study the decidability of termination of several variants of simple integer loops, without branching in the loop body and with affine constraints as the loop guard (and possibly a precondition). We show that termination of such loops is undecidable in some cases, in particular, when the body of the loop is expressed by a set of linear inequalities where the coefficients are from ℤ ∪ {r} with r an arbitrary irrational; or when the loop is a sequence of instructions, that compute either linear expressions or the step function. The undecidability result is proven by a reduction from counter programs, whose termination is known to be undecidable. For the common case of integer constraints loops with rational coefficients only we have not succeeded in proving decidability nor undecidability of termination, however, this attempt led to the result that a Petri net can be simulated with such a loop, which implies some interesting lower bounds. For example, termination for a given input is at least EXPSPACE-hard.

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Author information

Authors and Affiliations

  1. School of Computer Science, The Tel-Aviv Academic College, Israel

    Amir M. Ben-Amram

  2. DSIC, Complutense University of Madrid (UCM), Spain

    Samir Genaim

  3. DLSIIS, Technical University of Madrid (UPM), Spain

    Abu Naser Masud

Authors
  1. Amir M. Ben-Amram
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  2. Samir Genaim
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  3. Abu Naser Masud
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Editor information

Editors and Affiliations

  1. Swiss Federal Institute of Technology Lausanne (EPFL), IC IIF LARA INR 318, Station 14, 1015, Lausanne, Switzerland

    Viktor Kuncak

  2. Institut für Informatik, Technische Universität München, Boltzmannstr. 3, 85748, Munich, Germany

    Andrey Rybalchenko

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Ben-Amram, A.M., Genaim, S., Masud, A.N. (2012). On the Termination of Integer Loops. In: Kuncak, V., Rybalchenko, A. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2012. Lecture Notes in Computer Science, vol 7148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27940-9_6

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  • DOI: https://doi.org/10.1007/978-3-642-27940-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27939-3

  • Online ISBN: 978-3-642-27940-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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