On the complexity of finite, pushdown, and stack automata

Abstract

The complexity of predicates on several classes of formal languages is studied. For finite automata, pushdown automata, and several classes of stack automata, every nontrivial predicate on the languages accepted by the 1-way devices requires as much time and space as the recognition problem for any language accepted by the corresponding 2-way devices. Moreover there are nontrivial predicates on the languages accepted by the 1-way devices such that is the accepted language of some corresponding one or two head 2-way device. Thus our lower bounds are fairly tight.