Unique perfect matchings and proof nets

Lê Thành Dũng Nguyễn (1, 2)

1 DI-ENS - Département d'informatique - ENS Paris
2 LIPN - Laboratoire d'Informatique de Paris-Nord

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.

Domaines: Logique en informatique [cs.LO]; Algorithme et structure de données [cs.DS]; Complexité [cs.CC]

Lê Thành Dũng Nguyễn. Unique perfect matchings and proof nets. 2018. ⟨hal-01692179v1⟩