On the complexity of decidable cases of the commutation problem of languages

Document Type

Article

Publication Date

6-9-2005

Abstract

We investigate the complexity of basic decidable cases of the commutation problem for languages: testing the equality XY=YX for two languages X and Y. We show that it varies from co-NEXPTIME complete through PSPACE complete and co-NP complete to deterministic polynomial time, when Y is an explicitly given finite language and X is given by a CF grammar generating a finite language, a nondeterministic finite automaton (or a regular expression), an acyclic nondeterministic finite automaton or an explicitly given finite language, respectively. Interestingly in most cases the complexity status does not change if instead of explicitly given finite Y we consider general Y of the same type as X. For deterministic finite automata the problem remains open, due to the asymmetry of the catenation. © 2004 Elsevier B.V. All rights reserved.

Identifier

18444401433 (Scopus)

Publication Title

Theoretical Computer Science

External Full Text Location

https://doi.org/10.1016/j.tcs.2004.03.073

ISSN

03043975

First Page

105

Last Page

118

Issue

1-3

Volume

337

Grant

8T11C03915

Fund Ref

Academy of Finland

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