Some Results on Tape-Bounded Turing Machines

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Abstract
Classes of tape-bounded Turing machines similar to the on-line and off-line Turing machines, but without the restrictions that each machine halt and be deterministic, are studied. It is shown that the lower bounds on tape complexity of [1] depend on neither the halting assumption nor determinism. The existence of a dense hierarchy of complexity classes likewise does not depend on the halting assumption, and it is shown that below log n tape complexity there exists a dense hierarchy of complexity classes for two-way nondeterministic devices. It is also shown that the complexity classes of one-way, nondeterministic machines below linear large complexity are not closed under complementation and are larger that the corresponding deterministic complexity class.

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