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Complexity problems in real time computation

The study of computational complexity is continued under the additional requirement that the Turing machines operate in real time. The work reported here is motivated by that of Rabin [R] which asks implicitly about the computational power of n tape vs n+1 tape real time Turing machines and that of Hartmanis [H] who attempts a complexity measure for Turing machines in terms of reversals. The first result concerns itself with n tape real time Turing machines operating in a reversal bounded mode. A doubly infinite hierarchy (tapes-reversals) of classes of real time computable functions is shown to exist. The second result deals with n deterministic real time pushdown automata operating independently in parallel. It is shown that an increase in the number of pushdown automata operating in this manner always yields an increase in the computational power of the configuration.