A new correctness criterion for the proof nets of non-commutative multiplicative linear logics

Journal of Symbolic Logic 66 (4):1524-1542 (2001)
This paper presents a new correctness criterion for marked Danos-Reginer graphs (D-R graphs, for short) of Multiplicative Cyclic Linear Logic MCLL and Abrusci's non-commutative Linear Logic MNLL. As a corollary we obtain an affirmative answer to the open question whether a known quadratic-time algorithm for the correctness checking of proof nets for MCLL and MNLL can be improved to linear-time
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