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Recognizing pro-đ–± closures of regular languages

  • Jorge Almeida ORCID logo EMAIL logo , JosĂ© Carlos Costa ORCID logo and Marc Zeitoun ORCID logo
Published/Copyright: July 23, 2022

Abstract

Given a regular language L, we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary semigroups generated by the pseudovariety đ–± of all finite ℛ -trivial semigroups. In particular, we obtain a new effective solution of the separation problem of regular languages by đ–± -languages.

MSC 2010: 20M07; 20M35; 22A99

Communicated by Manfred Droste


Award Identifier / Grant number: UID/MAT/00144/2020

Award Identifier / Grant number: UIDB/00013/2020

Award Identifier / Grant number: UIDP/00013/2020

Award Identifier / Grant number: ANR-16-CE40-0007

Funding statement: This work was partly supported by the PESSOA French–Portuguese project “Separation in automata theory: algebraic, logical, and combinatorial aspects”. The work of the first two authors was also partially supported respectively by CMUP, member of LASI (project UID/MAT/00144/2020), and CMAT (projects UIDB/00013/2020 and UIDP/00013/2020), which are funded by FCT (Portugal) with national funds. The work of the third author was also partly supported by the DeLTA project ANR-16-CE40-0007.

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Received: 2019-06-23
Revised: 2022-04-12
Published Online: 2022-07-23
Published in Print: 2022-09-01

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