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Describing periodicity in two-way deterministic finite automata using transformation semigroups

Basic information
Original title:Describing periodicity in two-way deterministic finite automata using transformation semigroups
Authors:Michal Kunc, Alexander Okhotin
Further information
Citation:KUNC, Michal and Alexander OKHOTIN. Describing periodicity in two-way deterministic finite automata using transformation semigroups. In Giancarlo Mauri, Alberto Leporati. Developments in Language Theory: 15th International Conference, DLT 2011, Milan, Italy, July 19-22, 2011. Proceedings. Berlin: Springer, 2011. p. 324-336, 13 pp. ISBN 978-3-642-22320-4. doi:10.1007/978-3-642-22321-1_28.Export BibTeX
@inproceedings{961392,
author = {Kunc, Michal and Okhotin, Alexander},
address = {Berlin},
booktitle = {Developments in Language Theory: 15th International Conference, DLT 2011, Milan, Italy, July 19-22, 2011. Proceedings},
doi = {http://dx.doi.org/10.1007/978-3-642-22321-1_28},
editor = {Giancarlo Mauri, Alberto Leporati},
keywords = {finite automata; two-way deterministic automata; periodicity; transformation semigroups; unary languages},
language = {eng},
location = {Berlin},
isbn = {978-3-642-22320-4},
pages = {324-336},
publisher = {Springer},
title = {Describing periodicity in two-way deterministic finite automata using transformation semigroups},
year = {2011}
}
Original language:English
Field:General mathematics
Type:Article in Proceedings
Keywords:finite automata; two-way deterministic automata; periodicity; transformation semigroups; unary languages

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 max{G(n-l) + l + 1 | 0 <= l <= n} states, where G(k) is the maximum order of a permutation of k elements.

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