Remarks on Sorting and One-Way Multihead Finite Automata

Multihead one-way finite automata (l-MFA) received much attention in studies of devices of low complexity. This is because they work in linear time and because of their simplicity. On the other hand, the class of languages recognized by l-MFA is rather small. Anyway, it contains many languages important from the practical point of view. Despite the simplicity of l-MFA, many problems concerning them turned out to be not that simple. For instance, the question whether automata with k + 1 heads are more powerful than those with k heads, awaited long its solution (see [5,6,2,7,1]). Most languages recognized by l-MFA are in fact bounded languages (compare [l]), that is, languages L such that for some n