Hostname: page-component-cb9f654ff-5kfdg Total loading time: 0 Render date: 2025-09-07T16:52:28.633Z Has data issue: false hasContentIssue false
  • English
  • Français

On biautomata∗

Published online by Cambridge University Press:  19 June 2012

Ondřej Klíma  and
Libor Polák
Ondřej Klíma
Affiliation:
Department of Mathematics and Statistics, Masaryk University, Kotlrářská 2, 61137 Brno, Czech Republic. polak@math.muni.cz
Libor Polák
Affiliation:
Department of Mathematics and Statistics, Masaryk University, Kotlrářská 2, 61137 Brno, Czech Republic. polak@math.muni.cz
Get access

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.

Keywords

Biautomatacanonical biautomatonpiecewise testable languagesprefix-suffix languages

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Brzozowski, J., Derivatives of regular expressions. J. ACM 11 (1964) 481–494. Google Scholar
Klíma, O., Piecewise testable languages via combinatorics on words. Disc. Math. 311 (2011) 2124–2127. Google Scholar
Klíma, O. and Polák, L., On varieties of meet automata. Theoret. Comput. Sci. 407 (2008) 278–289. Google Scholar
Klíma, O. and Polák, L., Hierarchies of piecewise testable languages. Int. J. Found. Comput. Sci. 21 (2010) 517–533. Google Scholar
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.
J.-E. Pin, Varieties of Formal Languages. North Oxford, London and Plenum, New York (1986).
J.-E. Pin, Syntactic semigroups, in Handbook of Formal Languages, Chap. 10, edited by G. Rozenberg and A. Salomaa. Springer (1997).
Polák, L., Syntactic semiring and universal automata, in Proc. of DLT 2003. Lect. Notes Comput. Sci. 2710 (2003) 411–422. Google Scholar
I. Simon, Hierarchies of events of dot-depth one. Ph.D. thesis. University of Waterloo (1972).
Simon, I., Piecewise testable events, in Proc. of ICALP 1975. Lect. Notes Comput. Sci. 33 (1975) 214–222. Google Scholar