Abstract
The following statements are shown to be equivalent: (i) Every language accepted by a nondeterministic Turing machine which operates within time bound 2 cn for some c > 0 is also accepted by a deterministic Turing machine which operates within time bound 2 dn for some d > 0. (ii) Every tally language which is accepted by a nondeterministic polynomial time-bounded Turing machine is also accepted by a deterministic polynomial time bounded Turing machine. (iii) Every tally language which is accepted by a nondeterministic Turing machine which operates in real time is also accepted by a deterministic polynomial time bounded Turing machine. Other results concerning time‐space tradeoffs are presented. The results extend those in Book, 1972 , Book, 1974 , and Savitch (1973) . The proofs use the technique presented in Savitch (1973) .
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