Conversions Between Six Models of Finite Automata

Abstract

We examine the costs of the conversions between six automata models: deterministic finite automata, partial deterministic finite automata, nondeterministic finite automata with a unique final state and multiple final states, respectively, alternating finite automata, and Boolean finite automata. We present a tight upper bound for each conversion. All witnesses are described over a unary or binary alphabet, and we show that whenever a binary alphabet is used, it is always optimal.