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Head and state hierarchies for unary multi-head finite automata

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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.

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Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392 , Giessen, Germany

    Martin Kutrib, Andreas Malcher & Matthias Wendlandt

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  1. Martin Kutrib
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  2. Andreas Malcher
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  3. Matthias Wendlandt
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Correspondence to Andreas Malcher.

Additional information

A preliminary version has been published in the Proceedings of the 16th International Conference on Developments in Language Theory (DLT 2012).

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Kutrib, M., Malcher, A. & Wendlandt, M. Head and state hierarchies for unary multi-head finite automata. Acta Informatica 51, 553–569 (2014). https://doi.org/10.1007/s00236-014-0206-x

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  • DOI: https://doi.org/10.1007/s00236-014-0206-x

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