RAIRO - Theoretical Informatics and Applications

Research Article

Free group languages: Rational versus recognizable

Pedro V. Silva

Centro de Matemática, Faculdade de Ciências, Universidade do Porto, R. do Campo Alegre, 687, 4169-007 Porto, Portugal; pvsilva@fc.up.pt.


We provide alternative proofs and algorithms for results proved by Sénizergues on rational and recognizable free group languages. We consider two different approaches to the basic problem of deciding recognizability for rational free group languages following two fully independent paths: the symmetrification method (using techniques inspired by the study of inverse automata and inverse monoids) and the right stabilizer method (a general approach generalizable to other classes of groups). Several different algorithmic characterizations of recognizability are obtained, as well as other decidability results.

(Received November 26 2001)

(Accepted December 11 2003)

(Online publication March 15 2004)

Key Words:

  • Free group;
  • rational subsets;
  • recognizable subsets.

Mathematics Subject Classification:

  • 20E05;
  • 20F10;
  • 68Q45