A framework for the study of periodic behaviour of two-way deterministic finite automata (2DFA) is developed. Computations of 2DFAs are represented by a two-way analogue of transformation semigroups, every element of which describes the behaviour of a 2DFA on a certain string x. A subsemigroup generated by this element represents the behaviour on strings in x +. The main contribution of this paper is a description of all such monogenic subsemigroups up to isomorphism. This characterization is then used to show that transforming an n-state 2DFA over a one-letter alphabet to an equivalent sweeping 2DFA requires exactly n+1 states, and transforming it to a one-way automaton requires exactly states, where G(k) is the maximum order of a permutation of k elements. © 2011 Springer-Verlag.
CITATION STYLE
Kunc, M., & Okhotin, A. (2011). Describing periodicity in two-way deterministic finite automata using transformation semigroups. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6795 LNCS, pp. 324–336). https://doi.org/10.1007/978-3-642-22321-1_28
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