DECIDABILITY OF REGULAR LANGUAGE GENUS COMPUTATION - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Mathematical Structures in Computer Science Year : 2019


Guillaume Bonfante
  • Function : Author
  • PersonId : 864819


The article continues the study of the genus of regular languages that the authors introduced in a 2012 paper. Let L be a regular language. In order to understand the genus g(L) of L, we introduce the topological size of |L|top to be the minimal size of all finite deterministic automata of genus g(L) computing L. We show that the minimal finite deterministic automaton of a regular language can be arbitrary far away from a finite deterministic automaton realizing the minimal genus and computing the same language, both in terms of the difference of genera and in terms of the difference in size. We show that the topological size |L|top can grow at least exponentially in size |L|. We conjecture the genus of every regular language to be computable. This conjecture implies in particular that the planarity of a regular language is decidable, a question asked in 1978 by R.V. Book and A.K. Chandra. We prove here the conjecture for a fairly generic class of regular languages having no short cycles.
Fichier principal
Vignette du fichier
GenusLanguage.pdf (368.94 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03178810 , version 1 (24-03-2021)



Guillaume Bonfante, Florian Deloup. DECIDABILITY OF REGULAR LANGUAGE GENUS COMPUTATION. Mathematical Structures in Computer Science, 2019, 29 (9), pp.1428-1443. ⟨10.1017/S0960129519000057⟩. ⟨hal-03178810⟩
44 View
174 Download



Gmail Facebook X LinkedIn More