Department of Mathematics and Statistics, Masaryk University, Kotlrářská 2, 61137 Brno, Czech Republic
Received: 11 November 2011
Accepted: 3 May 2012
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.
Mathematics Subject Classification: 68Q70
Key words: Biautomata / canonical biautomaton / piecewise testable languages / prefix-suffix languages
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