Mathematical systems theory

, Volume 23, Issue 1, pp 107–139 | Cite as

One-way multihead finite automata and 2-bounded languages

  • Mirosław Kutyłowski


LanguagesL n ={1 x 2 ix :i, x ∈ ℕ, 1≤in} were used to show that, for eachk, one-way non-sensing deterministic finite automata (1-MFA) withk+1 heads are more powerful than such automata withk heads, even if we consider only 2-bounded languages (Chrobak). Fork ∈ ℕ letf(k) be the maximal numbern such that languageL n can be recognized by a 1-MFA withk heads. We present a precise inductive formula forf(k). It may be shown that, fork≥3,
$$\frac{{(2k - 5)! \cdot (k - 2) \cdot (k - 1)}}{{2^{k - 3} }} \leqslant f(k) \leqslant \frac{{(2k - 5)! \cdot (k - 2) \cdot (k - 1) \cdot 3k^2 }}{{2^{k - 3} }}$$
that is,f(k)≈k2k. The proof is constructive in the sense that it shows how to construct ak-head automaton recognizingL f(k) . This is a solution of the problem stated by Chrobak.


Computational Mathematic Finite Automaton Deterministic Finite Automaton Inductive Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Mirosław Kutyłowski
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

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