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Non-deterministic Boolean Proof Nets

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Foundational and Practical Aspects of Resource Analysis (FOPARA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6324))

Abstract

We introduce Non-deterministic Boolean proof nets to study the correspondence with Boolean circuits, a parallel model of computation. We extend the cut elimination of Non-deterministic Multiplicative Linear logic to a parallel procedure in proof nets. With the restriction of proof nets to Boolean types, we prove that the cut-elimination procedure corresponds to Non-deterministic Boolean circuit evaluation and reciprocally. We obtain implicit characterization of the complexity classes NP and NC (the efficiently parallelizable functions).

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Author information

Authors and Affiliations

  1. LIPN, UMR7030, CNRS, Université Paris 13, France

    Virgile Mogbil

Authors
  1. Virgile Mogbil
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Editors and Affiliations

  1. Institute for Computing and Information Sciences, Radboud Universiteit Nijmegen, P.O. Box 9102, 6500 HC, Nijmegen, The Netherlands

    Marko van Eekelen

  2. Institute for Computing and Information Sciences, Radboud University Nijmegen, The Netherlands

    Olha Shkaravska

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Mogbil, V. (2010). Non-deterministic Boolean Proof Nets. In: van Eekelen, M., Shkaravska, O. (eds) Foundational and Practical Aspects of Resource Analysis. FOPARA 2009. Lecture Notes in Computer Science, vol 6324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15331-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-15331-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15330-3

  • Online ISBN: 978-3-642-15331-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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