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.
Mots-clés : biautomata, canonical biautomaton, piecewise testable languages, prefix-suffix languages
@article{ITA_2012__46_4_573_0,
author = {Kl{\'\i}ma, Ond\v{r}ej and Pol\'ak, Libor},
title = {On biautomata},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {573--592},
publisher = {EDP-Sciences},
volume = {46},
number = {4},
year = {2012},
doi = {10.1051/ita/2012014},
mrnumber = {3107864},
zbl = {1279.68238},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita/2012014/}
}
TY - JOUR AU - Klíma, Ondřej AU - Polák, Libor TI - On biautomata JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2012 SP - 573 EP - 592 VL - 46 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2012014/ DO - 10.1051/ita/2012014 LA - en ID - ITA_2012__46_4_573_0 ER -
%0 Journal Article %A Klíma, Ondřej %A Polák, Libor %T On biautomata %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2012 %P 573-592 %V 46 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2012014/ %R 10.1051/ita/2012014 %G en %F ITA_2012__46_4_573_0
Klíma, Ondřej; Polák, Libor. On biautomata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 4, pp. 573-592. doi : 10.1051/ita/2012014. http://archive.numdam.org/articles/10.1051/ita/2012014/
[1] , Derivatives of regular expressions. J. ACM 11 (1964) 481-494. | MR | Zbl
[2] , Piecewise testable languages via combinatorics on words. Disc. Math. 311 (2011) 2124-2127. | MR | Zbl
[3] and , On varieties of meet automata. Theoret. Comput. Sci. 407 (2008) 278-289. | MR | Zbl
[4] and , Hierarchies of piecewise testable languages. Int. J. Found. Comput. Sci. 21 (2010) 517-533. | MR | Zbl
[5] and , 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. | MR | Zbl
[6] , Varieties of Formal Languages. North Oxford, London and Plenum, New York (1986). | MR | Zbl
[7] , Syntactic semigroups, in Handbook of Formal Languages, Chap. 10, edited by G. Rozenberg and A. Salomaa. Springer (1997). | MR | Zbl
[8] , Syntactic semiring and universal automata, in Proc. of DLT 2003. Lect. Notes Comput. Sci. 2710 (2003) 411-422. | MR | Zbl
[9] , Hierarchies of events of dot-depth one. Ph.D. thesis. University of Waterloo (1972). | MR
[10] , Piecewise testable events, in Proc. of ICALP 1975. Lect. Notes Comput. Sci. 33 (1975) 214-222. | MR | Zbl
Cité par Sources :
