On stateless multihead automata: Hierarchies and the emptiness problem

Authors:
Oscar H. Ibarra;Juhani Karhumäki;Alexander Okhotin
Affiliations:
Department of Computer Science, University of California, Santa Barbara, CA 93106, USA;Department of Mathematics, University of Turku, Turku, FI-20014, Finland;Department of Mathematics, University of Turku, Turku, FI-20014, Finland and Academy of Finland, Helsinki, Finland
Venue:
Theoretical Computer Science
Year:
2010

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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.