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International Conference on Typed Lambda Calculi and Applications

TLCA 2003: Typed Lambda Calculi and Applications pp 31–45Cite as

Max-Plus Quasi-interpretations

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2701))

Abstract

Quasi-interpretations are a tool to bound the size of the values computed by a first-order functional program (or a term rewriting system) and thus a mean to extract bounds on its computational complexity. We study the synthesis of quasi-interpretations selected in the space of polynomials over the max-plus algebra determined by the non-negative rationals extended with −∞ and equipped with binary operations for the maximum and the addition. We prove that in this case the synthesis problem is NP-hard, and in NP for the particular case of multi-linear quasi-interpretations when programs are specified by rules of bounded size. The relevance of multi-linear quasi-interpretations is discussed by comparison to certain syntactic and type theoretic conditions proposed in the literature to control time and space complexity.

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique Fondamentale, Marseille

    Roberto M. Amadio

Authors
  1. Roberto M. Amadio
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität München, Oettingenstr. 67, 80538, München, Germany

    Martin Hofmann

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© 2003 Springer-Verlag Berlin Heidelberg

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Amadio, R.M. (2003). Max-Plus Quasi-interpretations. In: Hofmann, M. (eds) Typed Lambda Calculi and Applications. TLCA 2003. Lecture Notes in Computer Science, vol 2701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44904-3_3

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  • DOI: https://doi.org/10.1007/3-540-44904-3_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40332-6

  • Online ISBN: 978-3-540-44904-1

  • eBook Packages: Springer Book Archive

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