Marshall, Andrew M and Meadows, Catherine and Narendran, Paliath - On Unification Modulo One-Sided Distributivity: Algorithms, Variants and Asymmetry

lmcs:1571 - Logical Methods in Computer Science, June 19, 2015, Volume 11, Issue 2
On Unification Modulo One-Sided Distributivity: Algorithms, Variants and Asymmetry

Authors: Marshall, Andrew M and Meadows, Catherine and Narendran, Paliath

An algorithm for unification modulo one-sided distributivity is an early result by Tid\'en and Arnborg. More recently this theory has been of interest in cryptographic protocol analysis due to the fact that many cryptographic operators satisfy this property. Unfortunately the algorithm presented in the paper, although correct, has recently been shown not to be polynomial time bounded as claimed. In addition, for some instances, there exist most general unifiers that are exponentially large with respect to the input size. In this paper we first present a new polynomial time algorithm that solves the decision problem for a non-trivial subcase, based on a typed theory, of unification modulo one-sided distributivity. Next we present a new polynomial algorithm that solves the decision problem for unification modulo one-sided distributivity. A construction, employing string compression, is used to achieve the polynomial bound. Lastly, we examine the one-sided distributivity problem in the new asymmetric unification paradigm. We give the first asymmetric unification algorithm for one-sided distributivity.


Source : oai:arXiv.org:1503.06687
DOI : 10.2168/LMCS-11(2:11)2015
Volume: Volume 11, Issue 2
Published on: June 19, 2015
Submitted on: May 19, 2014
Keywords: Computer Science - Logic in Computer Science


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