On Multi-Head Finite Automata

Let M
n
be the class of languages defined by n-head finite automata. The Boolean and Kleene closure properties of M
n
are investigated, and a relationship between M
n
and the class of sets of n-tuples of tapes defined by n-tape finite automata is established. It is shown that the classes M
i
form a hierarchy; and that, moreover, for all n, there is a context-free language (CFL) in M
n+1
−M
n
. It is further shown that there is a CFL which is in no M
n
for any integer n. Finally, several decision properties of the multi-head languages are established.