How expressions can code for automata
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 39 (2005) no. 1, p. 217-237

In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata. We show here that if an automaton is then sufficiently “decorated”, the combination of these two algorithms gives the desired result. Reducing the amount of “decoration” is still the object of ongoing investigation.

DOI : https://doi.org/10.1051/ita:2005013
Classification:  68Q45,  68Q70
Keywords: finite automata, regular expression, derivation of expressions, quotient of automata
@article{ITA_2005__39_1_217_0,
     author = {Lombardy, Sylvain and Sakarovitch, Jacques},
     title = {How expressions can code for automata},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {1},
     year = {2005},
     pages = {217-237},
     doi = {10.1051/ita:2005013},
     zbl = {1102.68070},
     mrnumber = {2132589},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2005__39_1_217_0}
}
Lombardy, Sylvain; Sakarovitch, Jacques. How expressions can code for automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 39 (2005) no. 1, pp. 217-237. doi : 10.1051/ita:2005013. http://www.numdam.org/item/ITA_2005__39_1_217_0/

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