ONE-WAY MULTIHEAD FINITE AUTOMATA AND 2-BOUNDED LANGUAGES

Languages Ln={1x2ix: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 Ln 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, {Mathematical expression} that is, f(k)≈k2k. The proof is constructive in the sense that it shows how to construct a k-head automaton recognizing Lf(k). This is a solution of the problem stated by Chrobak. © 1990 Springer-Verlag New York Inc.