On Biautomata

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Authors	KLÍMA Ondřej POLÁK Libor
Year of publication	2012
Type	Article in Periodical
Magazine / Source	RAIRO - Theoretical Informatics and Applications
MU Faculty or unit	Faculty of Science
Citation
Doi	http://dx.doi.org/10.1051/ita/2012014
Field	General mathematics
Keywords	Biautomata; piecewise testable languages
Description	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.
Related projects:	Mathematical structures and their physical applications Algebraic Methods in Automata and Formal Language Theory II