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Non-uniform Polytime Computation in the Infinitary Affine Lambda-Calculus

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Automata, Languages, and Programming (ICALP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8573))

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Abstract

We give an implicit, functional characterization of the class of non-uniform polynomial time languages, based on an infinitary affine lambda-calculus and on previously defined bounded-complexity subsystems of linear (or affine) logic. The fact that the characterization is implicit means that the complexity is guaranteed by structural properties of programs rather than explicit resource bounds. As a corollary, we obtain a proof of the (already known) P-completeness of the normalization problem for the affine lambda-calculus which mimics in an interesting way Ladner’s P-completeness proof of CIRCUIT VALUE (essentially, the argument giving the Cook-Levin theorem). This suggests that the relationship between affine and usual lambda-calculus is deeply similar to that between Boolean circuits and Turing machines.

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Author information

Authors and Affiliations

  1. CNRS, UMR 7030, LIPN, Université Paris 13, Sorbonne Paris Cité, France

    Damiano Mazza

Authors
  1. Damiano Mazza
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, 85748, München, Germany

    Javier Esparza

  2. LIAFA, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Pierre Fraigniaud

  3. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Thore Husfeldt

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

    Elias Koutsoupias

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Mazza, D. (2014). Non-uniform Polytime Computation in the Infinitary Affine Lambda-Calculus. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43951-7_26

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  • DOI: https://doi.org/10.1007/978-3-662-43951-7_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43950-0

  • Online ISBN: 978-3-662-43951-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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