Geometrical Closure of Binary \(V_{3/2}\) Languages

  • Jean-Philippe Dubernard
  • Giovanna Guaiana
  • Ludovic MignotEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11417)


We define the geometrical closure of a language over a \(j\)-ary alphabet, and we prove that in the case of dimension 2 the family \(V_{3/2}\) in the Straubing-Thérien hierarchy of languages is closed under this operation. In other words, the geometrical closure of a \(V_{3/2}\) binary language is still a \(V_{3/2}\) language. This is achieved by carrying out some transformations over a regular expression representing the \(V_{3/2}\) language, which leads to a \(V_{3/2}\) regular expression for the geometrical closure.


Regular language Geometrical language Regular expression Straubing-Thérien hierarchy 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jean-Philippe Dubernard
    • 1
  • Giovanna Guaiana
    • 1
  • Ludovic Mignot
    • 2
    Email author
  1. 1.LITIS EA 4108Université de Rouen NormandieSaint-Étienne-du-RouvrayFrance
  2. 2.GR²IFUniversité de Rouen NormandieSaint-Étienne-du-RouvrayFrance

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