On the power of real-time Turing machines: k tapes are more powerful than k \Gamma 1 tapes

We show that, for any integer k, there is at least one language which is accepted by ak-tape real{time Turing machine, but cannot be accepted by a (k, 1)-tape real{time Turing machine. We show therefore that the languages accepted by real{time Turing machines form an in nite hierarchy with respect to the number of tapes used.