Unique perfect matchings and proof nets

Author Lê Thành Dung Nguyen

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Lê Thành Dung Nguyen
  • Département d'informatique, École normale supérieure, Paris Sciences et Lettres , 45 rue d'Ulm, 75005 Paris, France, Université Paris 13, Sorbonne Paris Cité, LIPN, CNRS , 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France

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Lê Thành Dung Nguyen. Unique perfect matchings and proof nets. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Linear logic
  • Mathematics of computing → Matchings and factors
  • Mathematics of computing → Graph algorithms
  • correctness criteria
  • matching algorithms


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