Equivalence Testing of Weighted Automata over Partially Commutative Monoids
Abstract
We study \emph{multiplicity equivalence} testing of automata over partially commutative monoids (pc monoids) and show efficient algorithms in special cases, exploiting the structure of the underlying non-commutation graph of the monoid. Specifically, if the clique cover number of the non-commutation graph (the minimum number of cliques covering the graph) of the pc monoid is a constant, we obtain a deterministic quasi-polynomial time algorithm. As a consequence, we also obtain the first deterministic quasi-polynomial time algorithms for multiplicity equivalence testing of -tape automata and for equivalence testing of deterministic -tape automata for constant . Prior to this, a randomized polynomial-time algorithm for the above problems was shown by Worrell [ICALP 2013]. We also consider pc monoids for which the non-commutation graphs have cover consisting of at most cliques and star graphs for any constant . We obtain randomized polynomial-time algorithm for multiplicity equivalence testing of automata over such monoids.
Keywords
Cite
@article{arxiv.2002.08633,
title = {Equivalence Testing of Weighted Automata over Partially Commutative Monoids},
author = {V. Arvind and Abhranil Chatterjee and Rajit Datta and Partha Mukhopadhyay},
journal= {arXiv preprint arXiv:2002.08633},
year = {2020}
}