Mathematical systems theory

, Volume 23, Issue 1, pp 107–139

One-way multihead finite automata and 2-bounded languages

  • Mirosław Kutyłowski

DOI: 10.1007/BF02090769

Cite this article as:
Kutyłowski, M. Math. Systems Theory (1990) 23: 107. doi:10.1007/BF02090769


LanguagesLn={1x2ix: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 languageLn 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 recognizingLf(k). This is a solution of the problem stated by Chrobak.

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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