NONDETERMINISTIC BIAUTOMATA AND THEIR DESCRIPTIONAL COMPLEXITY

Abstract

We investigate the descriptional complexity of nondeterministic biautomata, which are a generalization of biautomata [O. KLÍMA, L. POLÁK: On biautomata. RAIRO — Theor. Inf. Appl., 46(4), 2012]. Simply speaking, biautomata are finite automata reading the input from both sides; although the head movement is nondeterministic, additional requirements enforce biautomata to work deterministically. First we study the size blow-up when determinizing nondeterministic biautomata. Further, we give tight bounds on the number of states for nondeterministic biautomata accepting regular languages relative to the size of ordinary finite automata, regular expressions, and syntactic monoids. It turns out that as in the case of ordinary finite automata nondeterministic biautomata are superior to biautomata with respect to their relative succinctness in representing regular languages.