. . . "Berlin" . "Describing periodicity in two-way deterministic finite automata using transformation semigroups"@en . "Okhotin, Alexander" . "13"^^ . . "2011-01-01+01:00"^^ . . "RIV/00216224:14310/11:00050221!RIV12-GA0-14310___" . . . . . "978-3-642-22320-4" . "[14307EAEAE52]" . "14310" . "Milan, Italy" . . . "P(GA201/09/1313), Z(MSM0021622409)" . "10.1007/978-3-642-22321-1_28" . . "Kunc, Michal" . . "Springer-Verlag" . . "1"^^ . . "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." . "Developments in Language Theory: 15th International Conference, DLT 2011, Milan, Italy, July 19-22, 2011. Proceedings" . "finite automata; two-way deterministic automata; periodicity; transformation semigroups; unary languages"@en . . . . "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."@en . "2"^^ . "Describing periodicity in two-way deterministic finite automata using transformation semigroups" . "193462" . . . "RIV/00216224:14310/11:00050221" . "Describing periodicity in two-way deterministic finite automata using transformation semigroups" . . "Describing periodicity in two-way deterministic finite automata using transformation semigroups"@en . "0302-9743" .