How expressions can code for automata

Sylvain Lombardy; Jacques Sakarovitch

RAIRO - Theoretical Informatics and Applications (2010)

  • 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 39.1 (2010): 217-237. <http://eudml.org/doc/92758>.

@article{Lombardy2010,
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},
keywords = {Finite automata; regular expression; derivation of expressions; quotient of automata.; derived term of an expression},
language = {eng},
month = {3},
number = {1},
pages = {217-237},
publisher = {EDP Sciences},
title = {How expressions can code for automata},
url = {http://eudml.org/doc/92758},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Lombardy, Sylvain
AU - Sakarovitch, Jacques
TI - How expressions can code for automata
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
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/92758
ER -

References

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  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.)  
  13. R. McNaughton and H. Yamada, Regular Expressions And State Graphs For Automata. IRE Trans. electronic computers9 (1960) 39–47.  
  14. J. Sakarovitch, A construction on automata that has remained hidden. Theor. Comput. Sci.204 (1998) 205–231.  
  15. J. Sakarovitch, Éléments de théorie des automates. Vuibert (2003). English Trans.: Cambridge University Press, to appear.  
  16. K. Thompson, Regular expression search algorithm. Comm. Assoc. Comput. Mach.11 (1968) 419–422.  
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  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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