Similarity relations and cover automata

Jean-Marc Champarnaud; Franck Guingne; Georges Hansel

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 39, Issue: 1, page 115-123
  • ISSN: 0988-3754

Abstract

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Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate consequences.

How to cite

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Champarnaud, Jean-Marc, Guingne, Franck, and Hansel, Georges. "Similarity relations and cover automata." RAIRO - Theoretical Informatics and Applications 39.1 (2010): 115-123. <http://eudml.org/doc/92749>.

@article{Champarnaud2010,
abstract = { Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate consequences. },
author = {Champarnaud, Jean-Marc, Guingne, Franck, Hansel, Georges},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Finite automata; cover automaton for a finite language; similarity relation},
language = {eng},
month = {3},
number = {1},
pages = {115-123},
publisher = {EDP Sciences},
title = {Similarity relations and cover automata},
url = {http://eudml.org/doc/92749},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Champarnaud, Jean-Marc
AU - Guingne, Franck
AU - Hansel, Georges
TI - Similarity relations and cover automata
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 1
SP - 115
EP - 123
AB - Cover automata for finite languages have been much studied a few years ago. It turns out that a simple mathematical structure, namely similarity relations over a finite set of words, is underlying these studies. In the present work, we investigate in detail for themselves the properties of these relations beyond the scope of finite languages. New results with straightforward proofs are obtained in this generalized framework, and previous results concerning cover automata are obtained as immediate consequences.
LA - eng
KW - Finite automata; cover automaton for a finite language; similarity relation
UR - http://eudml.org/doc/92749
ER -

References

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  1. C. Câmpeanu, N. Sântean and S. Yu, Minimal Cover-automata for Finite Languages. Theor. Comput. Sci.267 (2001) 3–16.  
  2. C. Câmpeanu, A. Păun and S. Yu, An Efficient Algorithm for Constructing Minimal Cover Automata for Finite Languages. Int. J. Foundations Comput. Sci.13-1 (2002) 99–113.  
  3. C. Dwork and L. Stockmeyer, A Time Complexity Gap for Two-Way Probabilistic Finite-State Automata. SIAM J. Comput.19 (1990) 1011–1023.  Zbl0711.68075
  4. J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation . Addison-Wesley, Reading MA (1979).  Zbl0426.68001
  5. J. Kaneps and R. Friedvalds, Running Time to Recognize Non-Regular Languages by 2-Way Probabilistic Automata, in ICALP'91. Lect. Notes Comput. Sci.510 (1991) 174–185.  Zbl0766.68098
  6. H. Körner, A Time and Space Efficient Algorithm for Minimizing Cover Automata for Finite Languages. Int. J. Foundations Comput. Sci.14 (2003) 1071–1086.  
  7. N. Sântean, Towards a Minimal Representation for Finite Languages: Theory and Practice. Master Thesis, The University of Western Ontario (2000).  
  8. S. Yu, Regular Languages, in Handbook of Formal Languages, edited by G. Rozenberg and A. Salomaa. Springer, Berlin (1997).  

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