States and heads do count for unary multi-head finite automata

Authors:
Martin Kutrib;Andreas Malcher;Matthias Wendlandt
Affiliations:
Institut für Informatik, Universität Giessen, Giessen, Germany;Institut für Informatik, Universität Giessen, Giessen, Germany;Institut für Informatik, Universität Giessen, Giessen, Germany
Venue:
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Year:
2012

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Hierarchies of one-way multihead automata languages

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On stateless multihead automata: Hierarchies and the emptiness problem

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Abstract

Unary deterministic one-way multi-head finite automata characterize the unary regular languages. Here they are studied with respect to the existence of head and state hierarchies. It turns out that for any fixed number of states, there is an infinite proper head hierarchy. In particular, the head hierarchy for stateless deterministic one-way multi-head finite automata is obtained using unary languages. On the other hand, it is shown that for a fixed number of heads, m+1 states are more powerful than m states. Finally, the open question of whether emptiness is undecidable for stateless one-way two-head finite automata is addressed and, as a partial answer, undecidability can be shown if at least four states are provided.