# One-way multihead finite automata and 2-bounded languages

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## Abstract

Languages that is,

*L*_{n}={1^{x}2^{ix}:*i, x*∈ ℕ, 1≤*i*≤*n*} were used to show that, for each*k*, one-way non-sensing deterministic finite automata (1-MFA) with*k*+1 heads are more powerful than such automata with*k*heads, even if we consider only 2-bounded languages (Chrobak). For*k*∈ ℕ let*f*(*k*) be the maximal number*n*such that language*L*_{n}can be recognized by a 1-MFA with*k*heads. We present a precise inductive formula for*f*(*k*). It may be shown that, for*k*≥3,$$\frac{{(2k - 5)! \cdot (k - 2) \cdot (k - 1)}}{{2^{k - 3} }} \leqslant f(k) \leqslant \frac{{(2k - 5)! \cdot (k - 2) \cdot (k - 1) \cdot 3k^2 }}{{2^{k - 3} }}$$

*f*(*k*)≈*k*^{2k}. The proof is constructive in the sense that it shows how to construct a*k*-head automaton recognizing*L*_{f(k)}. This is a solution of the problem stated by Chrobak.## Preview

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### References

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