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Complexity Bounds for Ordinal-Based Termination

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Reachability Problems (RP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8762))

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Abstract

‘What more than its truth do we know if we have a proof of a theorem in a given formal system?’ We examine Kreisel’s question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times.

Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.

1998 ACM Subject Classification. F.2.0 Analysis of Algorithms and Problem Complexity; F.3.1 Logics and Meanings of Programs

Work funded in part by the ANR grant 11-BS02-001-01 ReacHard.

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Author information

Authors and Affiliations

  1. LSV, ENS Cachan & CNRS & INRIA, France

    Sylvain Schmitz

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  1. Sylvain Schmitz
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Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Joël Ouaknine

  2. Department of Computer Science, University of Liverpool, Liverpool, UK

    Igor Potapov

  3. Department of Computer Science, University of Oxford, UK

    James Worrell

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Schmitz, S. (2014). Complexity Bounds for Ordinal-Based Termination. In: Ouaknine, J., Potapov, I., Worrell, J. (eds) Reachability Problems. RP 2014. Lecture Notes in Computer Science, vol 8762. Springer, Cham. https://doi.org/10.1007/978-3-319-11439-2_1

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  • DOI: https://doi.org/10.1007/978-3-319-11439-2_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11438-5

  • Online ISBN: 978-3-319-11439-2

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