Describing Periodicity in Two-Way Deterministic Finite Automata Using Transformation Semigroups [chapter]

Michal Kunc, Alexander Okhotin
2011 Lecture Notes in Computer Science  
A framework for the study of periodic behaviour of twoway 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
more » ... en 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 0 n G(n − ) + + 1 states, where G(k) is the maximum order of a permutation of k elements.
doi:10.1007/978-3-642-22321-1_28 fatcat:4xycfjbthncuterrsoigqdfhn4