States and Heads Do Count for Unary Multi-head Finite Automata

  • Martin Kutrib
  • Andreas Malcher
  • Matthias Wendlandt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7410)


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.


Cycle Length Finite Automaton Input Symbol State Hierarchy Longe Word 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Martin Kutrib
    • 1
  • Andreas Malcher
    • 1
  • Matthias Wendlandt
    • 1
  1. 1.Institut für InformatikUniversität GiessenGiessenGermany

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