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The word problem for omega-terms over the Trotter-Weil hierarchy
journal contribution
posted on 2018-02-22, 13:57 authored by Manfred Kufleitner, Jan Philipp Wachter© 2017 Springer Science+Business Media New York For two given ω-terms α and β, the word problem for ω-terms over a variety V asks whether α = β in all monoids in V. We show that the word problem for ω-terms over each level of the Trotter-Weil Hierarchy is decidable. More precisely, for every fixed variety in the Trotter-Weil Hierarchy, our approach yields an algorithm in nondeterministic logarithmic space (NL). In addition, we provide deterministic polynomial time algorithms which are more efficient than straightforward translations of the NL-algorithms. As an application of our results, we show that separability by the so-called corners of the Trotter-Weil Hierarchy is witnessed by ω-terms (this property is also known as ω-reducibility). In particular, the separation problem for the corners of the Trotter-Weil Hierarchy is decidable.
Funding
The first author was supported by the German Research Foundation (DFG) under grants DI 435/5-2 and KU 2716/1-1
History
School
- Science
Department
- Computer Science
Published in
Theory of Computing SystemsPages
1 - 57Citation
KUFLEITNER, M. and WACHTER, J.P., 2017. The Word Problem for Omega-Terms over the Trotter-Weil Hierarchy. Theory of Computing Systems, 62 (3), pp.682–738.Publisher
© SpringerVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2016-12-21Publication date
2017-05-16Notes
This is a post-peer-review, pre-copyedit version of an article published in Theory of Computing Systems. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00224-017-9763-z.ISSN
1432-4350eISSN
1433-0490Publisher version
Language
- en