Relations Between Time and Tape Complexities

Authors:
John E. Hopcroft;Jeffrey D. Ullman
Affiliations:
Cornell University, Ithaca, New York and Bell Telephone Laboratories, Inc., Murray Hill, New Jersey;Bell Telephone Laboratories, Inc., Murray Hill, New Jersey
Venue:
Journal of the ACM (JACM)
Year:
1968

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Abstract

It is shown that if a language L is recognized by a (nondeterministic) single-tape Turing machine of time complexity T(n), then L is recognized by a (nondeterministic) offline Turing machine of tape complexity T1/2(n). If T(n) ≥ n2;, L is recognized by a (nondeterministic) single-tape Turing machine of tape complexity T1/2(n). If a language L is recognized by a (nondeterministic) offline Turing machine of time complexity (T(n), then L is recognized by a (nondeterministic) offline Turing machine of tape complexity (T(n) log n)1/2 and by a (nondeterministic) single-tape Turing machine of that tape complexity if T (n) ≥ n2/log n.