In this simple model for a one-dimensional array of excitable cells, each site x E Z is in one of I), states: 0 (rested state) , 1 (excited state), 2, . .. ,1), 1 (refract ory states) . The states update in discrete t ime according to a synchronous rule: changes 1 ~ 2, . .. , I), 1 ~ 0 happen auto matically, while t he 0 ~ 1 change is induced by at least a threshold numb er of I s in t he local...

Article history: Received 28 June 2007 Revised 18 February 2008 Available online 6 June 2008

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...

We show that the size of a Las Vegas automaton and the size of a complete, minimal deterministic automaton accepting a regular language are polynomially related. More precisely, we show that if a regular language L is accepted by a Las Vegas automaton having r states such that the probability for a definite answer to occur is at least p, then r ≥ np, where n is the number of the states of the m...

We examine the succinctness of one-way, rotating, sweeping, and two-way deterministic finite automata (1dfas, rdfas, sdfas, 2dfas). Here, a sdfa is a 2dfa whose head can change direction only on the endmarkers and a rdfa is a sdfa whose head is reset on the left end of the input every time the right endmarker is read. We introduce a list of language operators and study the corresponding closure...

We examine the conjecture that no polynomial can upper bound the increase in the number of states when a one-way nondeterministic finite automaton (1nfa) is converted into an equivalent two-way deterministic finite automaton (2dfa). We study the problem of liveness, which admits 1nfas of polynomial size and is known to defy 2dfas of polynomial size if and only if the conjecture is true. We focu...