TY - GEN

T1 - Describing periodicity in two-way deterministic finite automata using transformation semigroups

AU - Kunc, Michal

AU - Okhotin, Alexander

PY - 2011/7/29

Y1 - 2011/7/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79960742191&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-22321-1_28

DO - 10.1007/978-3-642-22321-1_28

M3 - Conference contribution

AN - SCOPUS:79960742191

SN - 9783642223204

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 324

EP - 336

BT - Developments in Language Theory - 15th International Conference, DLT 2011, Proceedings

T2 - 15th International Conference on Developments in Language Theory, DLT 2011

Y2 - 19 July 2011 through 22 July 2011

ER -