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On Decidability of Intermediate Levels of Concatenation Hierarchies

  • Jorge Almeida
  • Jana Bartoňová
  • Ondřej Klíma
  • Michal KuncEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)

Abstract

It is proved that if definability of regular languages in the \(\Sigma _n\) fragment of the first-order logic on finite words is decidable, then it is decidable also for the \(\Delta _{n+1}\) fragment. In particular, the decidability for \(\Delta _5\) is obtained. More generally, for every concatenation hierarchy of regular languages, it is proved that decidability of one of its half levels implies decidability of the intersection of the following half level with its complement.

Keywords

Binary Relation Transitive Closure Regular Language Positive Variety Continuous Homomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jorge Almeida
    • 1
  • Jana Bartoňová
    • 2
  • Ondřej Klíma
    • 2
  • Michal Kunc
    • 2
    Email author
  1. 1.CMUP, Dep. Matemática, Faculdade de CiênciasUniversidade do PortoPortoPortugal
  2. 2.Department of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic

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