Computer Science > Formal Languages and Automata Theory
[Submitted on 20 Feb 2020 (v1), last revised 31 May 2020 (this version, v2)]
Title:Equivalence Testing of Weighted Automata over Partially Commutative Monoids
View PDFAbstract: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 $k$-tape automata and for equivalence testing of deterministic $k$-tape automata for constant $k$. 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 $k$ cliques and star graphs for any constant $k$. We obtain randomized polynomial-time algorithm for multiplicity equivalence testing of automata over such monoids.
Submission history
From: Abhranil Chatterjee [view email][v1] Thu, 20 Feb 2020 09:27:09 UTC (854 KB)
[v2] Sun, 31 May 2020 14:34:54 UTC (116 KB)
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