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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
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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
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 4: Special Issue: Non-Classical Models of Automata and Applications III (NCMA-2011) , October 2012 , pp. 573 - 592
Copyright
© EDP Sciences 2012

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