On stateless multihead automata: Hierarchies and the emptiness problem

Abstract

We look at stateless multihead finite automata in their two-way and one-way, deterministic and nondeterministic variations. The transition of a k -head automaton depends solely on the symbols currently scanned by its k heads, and every such transition moves each head one cell left or right, or instructs it to stay. We show that stateless ( k + 4 ) -head two-way automata are more powerful than stateless k -head two-way automata. In the one-way case, we prove a tighter result: stateless ( k + 1 ) -head one-way automata are more powerful than stateless k -head one-way automata. Finally, we show that the emptiness problem for stateless 2-head two-way automata is undecidable.