Unique perfect matchings and proof nets

Abstract : This paper establishes a bridge between linear logic and mainstream graph theory, building previous work by Retoré (2003). We show that the problem of correctness for MLL+Mix proof nets is equivalent to the problem of uniqueness of a perfect matching. By applying matching theory, we obtain new results for MLL+Mix proof nets: a linear-time correctness criterion, a quasi-linear sequentialization algorithm, and a characterization of the sub-polynomial complexity of the correctness problem. We also use graph algorithms to compute the dependency relation of Bagnol et al. (2015) and the kingdom ordering of Bellin (1997), and relate them to the notion of blossom which is central to combinatorial maximum matching algorithms.
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Communication dans un congrès
3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018), Jul 2018, Oxford, United Kingdom. 〈10.4230/LIPIcs.FSCD.2018.25〉
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https://hal.archives-ouvertes.fr/hal-01692179
Contributeur : Lê Thành Dũng Nguyễn <>
Soumis le : mardi 10 juillet 2018 - 02:35:00
Dernière modification le : jeudi 12 juillet 2018 - 01:33:35

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LIPIcs-FSCD-2018-25.pdf
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Lê Thành Dũng Nguyễn. Unique perfect matchings and proof nets. 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018), Jul 2018, Oxford, United Kingdom. 〈10.4230/LIPIcs.FSCD.2018.25〉. 〈hal-01692179v2〉

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