Free group languages : rational versus recognizable
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 38 (2004) no. 1, p. 49-67

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.

DOI : https://doi.org/10.1051/ita:2004003
Classification:  20E05,  20F10,  68Q45
Keywords: free group, rational subsets, recognizable subsets
@article{ITA_2004__38_1_49_0,
     author = {Silva, Pedro V.},
     title = {Free group languages : rational versus recognizable},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {1},
     year = {2004},
     pages = {49-67},
     doi = {10.1051/ita:2004003},
     zbl = {1082.68071},
     mrnumber = {2059028},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2004__38_1_49_0}
}
Silva, Pedro V. Free group languages : rational versus recognizable. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 38 (2004) no. 1, pp. 49-67. doi : 10.1051/ita:2004003. http://www.numdam.org/item/ITA_2004__38_1_49_0/

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