New algorithms for unification modulo one-sided distributivity and its variants

Authors:
Andrew M. Marshall;Paliath Narendran
Affiliations:
College of Computing and Information, Computer Science Department, University at Albany---SUNY;College of Computing and Information, Computer Science Department, University at Albany---SUNY
Venue:
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Year:
2012

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Abstract

An algorithm for unification modulo one-sided distributivity is an early result by Tiden and Arnborg [14]. Unfortunately the algorithm presented in the paper, although correct, has recently been shown not to be polynomial time bounded as claimed [11]. 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.