Descriptional complexity of biautomata

Authors:
Galina Jirásková;Ondřej Klíma
Affiliations:
Mathematical Institute, Slovak Academy of Sciences, Košice, Slovak Republic;Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic
Venue:
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Year:
2012

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Abstract

A biautomaton is a finite automaton which arbitrarily alternates between reading the input word from the left and from the right. Some compatibility assumptions in the formal definition of a biautomaton ensure that the acceptance of an input does not depend on the way how the input is read. The paper studies the constructions of biautomata from the descriptional point of view. It proves that the tight bounds on the size of a biautomaton recognizing a regular language represented by a deterministic or nondeterministic automaton of n states, or by a syntactic monoid of size n, are n·2n−2(n−1), 22n−2(2n−1), and n2, respectively.