## Paper: Dominator Trees and Fast Verification of Proof Nets (at LICS 2000)

**Andrzej S. Murawski C.-H. Luke Ong**

### Abstract

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.

### BibTeX

@InProceedings{MurawskiOng-DominatorTreesandFa, author = {Andrzej S. Murawski and C.-H. Luke Ong}, title = {Dominator Trees and Fast Verification of Proof Nets}, booktitle = {Proceedings of the Fifteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2000)}, year = {2000}, month = {June}, pages = {181--191}, location = {Santa Barbara, CA, USA}, publisher = {IEEE Computer Society Press} }