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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 30, Issue 3


The ω-inequality problem for concatenation hierarchies of star-free languages

Jorge AlmeidaORCID iD: http://orcid.org/0000-0002-3829-2382 / Ondřej Klíma / Michal Kunc
Published Online: 2017-09-06 | DOI: https://doi.org/10.1515/forum-2016-0028


The problem considered in this paper is whether an inequality of ω-terms is valid in a given level of a concatenation hierarchy of star-free languages. The main result shows that this problem is decidable for all (integer and half) levels of the Straubing–Thérien hierarchy.

Keywords: Pseudovariety; relatively free profinite semigroup; ordered monoid; concatenation hierarchy; Straubing–Thérien hierarchy

MSC 2010: 20M05; 20M07; 20M35; 68Q70


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About the article

Received: 2016-02-01

Revised: 2017-05-23

Published Online: 2017-09-06

Published in Print: 2018-05-01

Funding Source: Centro de Matemática Universidade do Porto

Award identifier / Grant number: UID/MAT/00144/2013

Funding Source: Fundação para a Ciência e a Tecnologia

Award identifier / Grant number: UID/MAT/00144/2013

Funding Source: Ministério da Ciência, Tecnologia e Ensino Superior

Award identifier / Grant number: UID/MAT/00144/2013

Funding Source: European Regional Development Fund

Award identifier / Grant number: UID/MAT/00144/2013

The first author was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MCTES) and European structural funds (FEDER), under the partnership agreement PT2020. The second and third authors were partially supported by the grant 15-02862S of the Grant Agency of the Czech Republic.

Citation Information: Forum Mathematicum, Volume 30, Issue 3, Pages 663–679, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2016-0028.

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