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International Conference on Tools and Algorithms for the Construction and Analysis of Systems

TACAS 2012: Tools and Algorithms for the Construction and Analysis of Systems pp 252–266Cite as

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Deciding Conditional Termination

Deciding Conditional Termination

  • Marius Bozga18,
  • Radu Iosif18 &
  • Filip Konečný18,19 
  • Conference paper
  • 1680 Accesses

  • 20 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7214)

Abstract

This paper addresses the problem of conditional termination, which is that of defining the set of initial configurations from which a given program terminates. First we define the dual set, of initial configurations, from which a non-terminating execution exists, as the greatest fixpoint of the pre-image of the transition relation. This definition enables the representation of this set, whenever the closed form of the relation of the loop is definable in a logic that has quantifier elimination. This entails the decidability of the termination problem for such loops. Second, we present effective ways to compute the weakest precondition for non-termination for difference bounds and octagonal (non-deterministic) relations, by avoiding complex quantifier eliminations. We also investigate the existence of linear ranking functions for such loops. Finally, we study the class of linear affine relations and give a method of under-approximating the termination precondition for a non-trivial subclass of affine relations. We have performed preliminary experiments on transition systems modeling real-life systems, and have obtained encouraging results.

Keywords

  • Ranking Function
  • Transition Relation
  • Atomic Proposition
  • Policy Iteration
  • Constraint Graph

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was supported by the French National Project ANR-09-SEGI-016 VERIDYC, by the Czech Science Foundation (projects P103/10/0306 and 102/09/H042), the Czech Ministry of Education (projects COST OC10009 and MSM 0021630528), the Barrande project MEB021023, and the EU/Czech IT4Innovations Centre of Excellence CZ.1.05/1.1.00/02.0070.

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Author information

Authors and Affiliations

  1. VERIMAG, CNRS, 2 av. de Vignate, 38610, Gières, France

    Marius Bozga, Radu Iosif & Filip Konečný

  2. IT4Innovations Centre of Excellence, FIT BUT, Czech Republic

    Filip Konečný

Authors
  1. Marius Bozga
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  2. Radu Iosif
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  3. Filip Konečný
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Editor information

Editors and Affiliations

  1. University of California at Santa Cruz, 1156 High Street, 95064, Santa Cruz, CA, USA

    Cormac Flanagan

  2. Fakultät für Ingenieurwesen, Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, Lotharstraße 65, 47057, Duisburg, Germany

    Barbara König

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Bozga, M., Iosif, R., Konečný, F. (2012). Deciding Conditional Termination. In: Flanagan, C., König, B. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2012. Lecture Notes in Computer Science, vol 7214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28756-5_18

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