Theoretical Computer Science
From proof-nets to interaction nets
Proceedings of the workshop on Advances in linear logic
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Theoretical Computer Science
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Correctness of Multiplicative Proof Nets is Linear
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Dominator Trees and Fast Verification of Proof Nets
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Fast verification of MLL proof nets via IMLL
ACM Transactions on Computational Logic (TOCL)
Correctness of multiplicative (and exponential) proof structures is NL-complete
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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The paper presents in full detail the first linear algorithm given in the literature (Guerrini (1999) [6]) implementing proof structure correctness for multiplicative linear logic without units. The algorithm is essentially a reformulation of the Danos contractibility criterion in terms of a sort of unification. As for term unification, a direct implementation of the unification criterion leads to a quasi-linear algorithm. Linearity is obtained after observing that the disjoint-set union-find at the core of the unification criterion is a special case of union-find with a real linear time solution.