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. © 2012 Springer-Verlag.
CITATION STYLE
Kutrib, M., Malcher, A., & Wendlandt, M. (2012). States and heads do count for unary multi-head finite automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7410 LNCS, pp. 214–225). https://doi.org/10.1007/978-3-642-31653-1_20
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