How expressions can code for automata

Sylvain Lombardy; Jacques Sakarovitch

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2005)

  • Volume: 39, Issue: 1, page 217-237
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Lombardy, Sylvain, and Sakarovitch, Jacques. "How expressions can code for automata." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.1 (2005): 217-237. <http://eudml.org/doc/245014>.

@article{Lombardy2005,
abstract = {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.},
author = {Lombardy, Sylvain, Sakarovitch, Jacques},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {finite automata; regular expression; derivation of expressions; quotient of automata; derived term of an expression},
language = {eng},
number = {1},
pages = {217-237},
publisher = {EDP-Sciences},
title = {How expressions can code for automata},
url = {http://eudml.org/doc/245014},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Lombardy, Sylvain
AU - Sakarovitch, Jacques
TI - How expressions can code for automata
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 1
SP - 217
EP - 237
AB - 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.
LA - eng
KW - finite automata; regular expression; derivation of expressions; quotient of automata; derived term of an expression
UR - http://eudml.org/doc/245014
ER -

References

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  12. [12] S. Lombardy and J. Sakarovitch, Derivatives of rational expressions with multiplicity. Theor. Comput. Sci., to appear. (Journal version of Proc. MFCS 02, Lect. Notes Comput. Sci. 2420 (2002) 471–482.) Zbl1014.68085
  13. [13] R. McNaughton and H. Yamada, Regular Expressions And State Graphs For Automata. IRE Trans. electronic computers 9 (1960) 39–47. Zbl0156.25501
  14. [14] J. Sakarovitch, A construction on automata that has remained hidden. Theor. Comput. Sci. 204 (1998) 205–231. Zbl0913.68137
  15. [15] J. Sakarovitch, Éléments de théorie des automates. Vuibert (2003). English Trans.: Cambridge University Press, to appear. 
  16. [16] K. Thompson, Regular expression search algorithm. Comm. Assoc. Comput. Mach. 11 (1968) 419–422. Zbl0164.46205
  17. [17] D. Wood, Theory Of Computation. Wiley (1987). Zbl0734.68001MR1094567
  18. [18] S. Yu, Regular languages, in Handbook of Formal Languages, edited by G. Rozenberg and A. Salomaa. Elsevier 1 (1997) 41–111. 

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