Corrigendum to our paper: How Expressions Can Code for Automata

Sylvain Lombardy; Jacques Sakarovitch

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 44, Issue: 3, page 339-361
  • ISSN: 0988-3754

Abstract

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In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the property was flawed. We give here the correct definition of the broken derived terms of an expression which allow to define the automaton and the detailed full proof of the property.

How to cite

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Lombardy, Sylvain, and Sakarovitch, Jacques. "Corrigendum to our paper: How Expressions Can Code for Automata." RAIRO - Theoretical Informatics and Applications 44.3 (2010): 339-361. <http://eudml.org/doc/250697>.

@article{Lombardy2010,
abstract = { In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the property was flawed. We give here the correct definition of the broken derived terms of an expression which allow to define the automaton and the detailed full proof of the property. },
author = {Lombardy, Sylvain, Sakarovitch, Jacques},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Finite automata; regular expression; derivation of expressions; quotient of automata.; finite automata; derivation of expressions; quotient of automata},
language = {eng},
month = {10},
number = {3},
pages = {339-361},
publisher = {EDP Sciences},
title = {Corrigendum to our paper: How Expressions Can Code for Automata},
url = {http://eudml.org/doc/250697},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Lombardy, Sylvain
AU - Sakarovitch, Jacques
TI - Corrigendum to our paper: How Expressions Can Code for Automata
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/10//
PB - EDP Sciences
VL - 44
IS - 3
SP - 339
EP - 361
AB - In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the property was flawed. We give here the correct definition of the broken derived terms of an expression which allow to define the automaton and the detailed full proof of the property.
LA - eng
KW - Finite automata; regular expression; derivation of expressions; quotient of automata.; finite automata; derivation of expressions; quotient of automata
UR - http://eudml.org/doc/250697
ER -

References

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  1. P.-Y. Angrand, S. Lombardy and J. Sakarovitch, On the number of broken derived terms of a rational expression. J. Automata, Languages and Combinatorics, to appear.  
  2. V. Antimirov, Partial derivatives of regular expressions and finite automaton constructions. Theoret. Computer Sci.155 (1996) 291–319.  Zbl0872.68120
  3. J.A. Brzozowski, Derivatives of regular expressions. J. Assoc. Comput. Mach.11 (1964) 481–494.  Zbl0225.94044
  4. P. Caron and M. Flouret, Glushkov construction for series: the non commutative case. Int. J. Comput. Math.80 (2003) 457–472.  Zbl1033.68058
  5. S. Eilenberg, Automata, Languages, and Machines.A, Academic Press (1974).  
  6. V. Glushkov, The abstract theory of automata. Russ. Math. Surv.16 (1961) 1–53.  Zbl0104.35404
  7. S. Lombardy and J. Sakarovitch, Derivatives of rational expressions with multiplicity. Theoret. Computer Sci.332 (2005) 141–177. (Journal version of Proc. MFCS 02, LNCS 2420 (2002) 471–482.)  Zbl1070.68074
  8. S. Lombardy and J. Sakarovitch, How expressions can code for automata. RAIRO – Inform. theor. appl.39 (2005) 217–237 (Journal version Proc. LATIN, LNCS 2976 (2004) 242–251.)  Zbl1102.68070
  9. J. Sakarovitch, Éléments de théorie des automates. Vuibert (2003), Corrected English edition: Elements of Automata Theory . Cambridge University Press (2009).  

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