A Note On the Hierarchy of One-way Data-Independent Multi-Head Finite Automata

In this paper we deal with one-way multi-head data-independent finite automata. A k-head finite automaton A is data-independent, if the position of every head i after step t in the computation on an input w is a function that depends only on the length of the input w, on i and on t (i.e. the trajectories of heads must be the same on the inputs of the same length). It is known that k(k + 1)/2 + 4 heads are better than k for one-way k-head data-independent finite automata. We improve here this result by showing that 2k + 2 heads are better than √ 2k heads for such automata.