Path-bounded one-way multihead finite automata

For each positive integer r greater than or equal to 1, a nondeterministic machine M is r path-bounded if for any input word x, there are r computation paths of M on x. This paper investigates the accepting powers of pathbounded one-way (simple) multihead nondeterministic finite automata. It is shown, that for each k greater than or equal to 2 and r greater than or equal to 1, there is a language accepted by an (r + 1), path-bounded one-way nondeterministic k head finite automaton, but not accepted by any r path-bounded one-way nondeterministic k head finite automaton whether or not simple.