# 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

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topLombardy, 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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- 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
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- J. Sakarovitch, A construction on automata that has remained hidden. Theor. Comput. Sci.204 (1998) 205–231. Zbl0913.68137
- J. Sakarovitch, Éléments de théorie des automates. Vuibert (2003). English Trans.: Cambridge University Press, to appear. Zbl1178.68002
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- 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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