A linear algorithm for finding dominators in flow graphs and related problems
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A new, simpler linear-time dominators algorithm
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A fast algorithm for finding dominators in a flowgraph
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Correctness of Multiplicative Proof Nets is Linear
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Dominator Trees and Fast Verification of Proof Nets
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Dominator Trees and Fast Verification of Proof Nets
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Fast verification of MLL proof nets via IMLL
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A linear algorithm for MLL proof net correctness and sequentialization
Theoretical Computer Science
Correctness of linear logic proof structures is NL-complete
Theoretical Computer Science
Correctness of multiplicative (and exponential) proof structures is NL-complete
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LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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We consider the following decision problems: ProofNet: Given a multiplicative linear logic (MLL) proof structure, is it a proof net? EssNet: Given an essential net (of an intuitionistic MLL sequent), is it correct?In this paper, we show that linear-time algorithms for EssNet can be obtained by constructing the dominator tree of the input essential net. As a corollary, by showing that ProofNet is linear-time reducible to EssNet (by the trip translation), we obtain a linear-time algorithm for ProofNet. We show further that these linear-time algorithms can be optimized to simple one-pass algorithms - each node of the input structure is visited at most once. As another application of dominator trees, we obtain linear-time algorithms for the problems of sequentializing proof nets (i.e. given a proof net, find a derivation for the underlying MLL sequent) and essential nets.