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A Formal Model for a Linear Time Correctness Condition of Proof Nets of Multiplicative Linear Logic

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Logic-Based Program Synthesis and Transformation (LOPSTR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12561))

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Abstract

In a previous paper, we have reported a new linear time correctness condition for proof nets of Multiplicative Linear Logic without units, where we gave a description of the algorithm in an informal way. In this paper, we give a formal model for the algorithm. Our formal model is based on a finite state transition system with queues as well as union-find trees as data structures. The model has been obtained by trial and error based on a concrete implementation of the algorithm. In addition, the algorithm has a subtle mechanism in order to avoid deadlock. We give an invariant property of the state transition system and it guarantees the deadlock-freedom.

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Authors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8561, Japan

    Satoshi Matsuoka

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  1. Satoshi Matsuoka
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Correspondence to Satoshi Matsuoka .

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Editors and Affiliations

  1. King’s College London, London, UK

    Maribel Fernández

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Matsuoka, S. (2021). A Formal Model for a Linear Time Correctness Condition of Proof Nets of Multiplicative Linear Logic. In: Fernández, M. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2020. Lecture Notes in Computer Science(), vol 12561. Springer, Cham. https://doi.org/10.1007/978-3-030-68446-4_16

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  • DOI: https://doi.org/10.1007/978-3-030-68446-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68445-7

  • Online ISBN: 978-3-030-68446-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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