On monogenic nondeterministic automata

Abstract

A finite automaton is said to be directable if it has an input word, a directing word, which takes it from every state into the same state. For nondeterministic (n.d.) automata, directability can be generalized in several ways, three such notions, D1-, D2-, and D3-directability, are used. In this paper, we consider monogenic n.d. automata, and for each i = 1,2,3, we present sharp bounds for the maximal lengths of the shortest Di-directing words.