On biautomata

Ondřej Klíma; Libor Polák

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2012)

  • Volume: 46, Issue: 4, page 573-592
  • ISSN: 0988-3754

Abstract

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We initiate the theory and applications of biautomata. A biautomaton can read a word alternately from the left and from the right. We assign to each regular language L its canonical biautomaton. This structure plays, among all biautomata recognizing the language L, the same role as the minimal deterministic automaton has among all deterministic automata recognizing the language L. We expect that from the graph structure of this automaton one could decide the membership of a given language for certain significant classes of languages. We present the first two results of this kind: namely, a language L is piecewise testable if and only if the canonical biautomaton of L is acyclic. From this result Simon’s famous characterization of piecewise testable languages easily follows. The second class of languages characterizable by the graph structure of their biautomata are prefix-suffix testable languages.

How to cite

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Klíma, Ondřej, and Polák, Libor. "On biautomata." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 46.4 (2012): 573-592. <http://eudml.org/doc/272989>.

@article{Klíma2012,
abstract = {We initiate the theory and applications of biautomata. A biautomaton can read a word alternately from the left and from the right. We assign to each regular language L its canonical biautomaton. This structure plays, among all biautomata recognizing the language L, the same role as the minimal deterministic automaton has among all deterministic automata recognizing the language L. We expect that from the graph structure of this automaton one could decide the membership of a given language for certain significant classes of languages. We present the first two results of this kind: namely, a language L is piecewise testable if and only if the canonical biautomaton of L is acyclic. From this result Simon’s famous characterization of piecewise testable languages easily follows. The second class of languages characterizable by the graph structure of their biautomata are prefix-suffix testable languages.},
author = {Klíma, Ondřej, Polák, Libor},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {biautomata; canonical biautomaton; piecewise testable languages; prefix-suffix languages},
language = {eng},
number = {4},
pages = {573-592},
publisher = {EDP-Sciences},
title = {On biautomata},
url = {http://eudml.org/doc/272989},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Klíma, Ondřej
AU - Polák, Libor
TI - On biautomata
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2012
PB - EDP-Sciences
VL - 46
IS - 4
SP - 573
EP - 592
AB - We initiate the theory and applications of biautomata. A biautomaton can read a word alternately from the left and from the right. We assign to each regular language L its canonical biautomaton. This structure plays, among all biautomata recognizing the language L, the same role as the minimal deterministic automaton has among all deterministic automata recognizing the language L. We expect that from the graph structure of this automaton one could decide the membership of a given language for certain significant classes of languages. We present the first two results of this kind: namely, a language L is piecewise testable if and only if the canonical biautomaton of L is acyclic. From this result Simon’s famous characterization of piecewise testable languages easily follows. The second class of languages characterizable by the graph structure of their biautomata are prefix-suffix testable languages.
LA - eng
KW - biautomata; canonical biautomaton; piecewise testable languages; prefix-suffix languages
UR - http://eudml.org/doc/272989
ER -

References

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  1. [1] J. Brzozowski, Derivatives of regular expressions. J. ACM11 (1964) 481–494. Zbl0225.94044MR174434
  2. [2] O. Klíma, Piecewise testable languages via combinatorics on words. Disc. Math.311 (2011) 2124–2127. Zbl1227.68086MR2825655
  3. [3] O. Klíma and L. Polák, On varieties of meet automata. Theoret. Comput. Sci.407 (2008) 278–289. Zbl1154.68070MR2463014
  4. [4] O. Klíma and L. Polák, Hierarchies of piecewise testable languages. Int. J. Found. Comput. Sci.21 (2010) 517–533. Zbl1205.68206MR2678186
  5. [5] S. Lombardy and J. Sakarovich, The universal automaton, in Logic and Automata : History and Perspectives, edited by J. Flum, E. Grödel and T. Wilke. Amsterdam University Press (2007) 457–504. Zbl1217.68133MR2508751
  6. [6] J.-E. Pin, Varieties of Formal Languages. North Oxford, London and Plenum, New York (1986). Zbl0632.68069MR912694
  7. [7] J.-E. Pin, Syntactic semigroups, in Handbook of Formal Languages, Chap. 10, edited by G. Rozenberg and A. Salomaa. Springer (1997). Zbl0866.68057MR1470002
  8. [8] L. Polák, Syntactic semiring and universal automata, in Proc. of DLT 2003. Lect. Notes Comput. Sci. 2710 (2003) 411–422. Zbl1037.68099MR2054382
  9. [9] I. Simon, Hierarchies of events of dot-depth one. Ph.D. thesis. University of Waterloo (1972). MR2623305
  10. [10] I. Simon, Piecewise testable events, in Proc. of ICALP 1975. Lect. Notes Comput. Sci. 33 (1975) 214–222. Zbl0316.68034MR427498

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