On three-way two-dimensional multicounter automata

Abstract

In this paper several problems concerning three-way two-dimensional multicounter automata are solved. It is shown that the class of languages accepted by L( m) counter-bounded multicounter automata is equal to the class of languages accepted by log L( m) space-bounded Turing machines for any natural function L( m). It is shown that for every r ⩾ 1 there exists an infinite hierarchy, with respect to the number of counters, of languages accepted by m r -bounded (deterministic or nondeterministic) multicounter automata. It is also shown that for any k ⩾ 2 there is an infinite hierarchy, with respect to the capacity of the counters, of languages accepted by deterministic k-counter automata. Finally it is shown that the class of languages accepted by three-way L( m)-bounded k-counter automata is not closed under row or column cyclic closure if L( m) = m, L( m) = m 2, or log L( m) = o(log m). Only square inputs are considered.