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Computational Complexity of One-Tape Turing Machine Computations

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J. HartmanisAuthors Info & Claims

Journal of the ACM (JACM), Volume 15, Issue 2

Pages 325 - 339

https://doi.org/10.1145/321450.321464

Published: 01 April 1968 Publication History

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Abstract

The quantitative aspects of one-tape Turing machine computations are considered. It is shown, for instance, that there exists a sharp time bound which must be reached for the recognition of nonregular sets of sequences. It is shown that the computation time can be used to characterize the complexity of recursive sets of sequences, and several results are obtained about this classification. These results are then applied to the recognition speed of context-free languages and it is shown, among other things, that it is recursively undecidable how much time is required to recognize a nonregular context-free language on a one-tape Turing machine. Several unsolved problems are discussed.

References

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LEWIS, P. M., STEARNS, R. E., AND HARTMANIS, J. Memory bolmds for recognition of con{ext-free and context-serYsitive languages. IEEE Conference llecord on Switching Circuit Theory and Logical Design, IEEE Pub. 16C13, 1965, pit. 191 202.

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Index Terms

Computational Complexity of One-Tape Turing Machine Computations
1. Theory of computation
  1. Formal languages and automata theory
    1. Grammars and context-free languages
  2. Models of computation
    1. Computability
      1. Turing machines

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Published In

Journal of the ACM Volume 15, Issue 2

April 1968

175 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321450

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 April 1968

Published in JACM Volume 15, Issue 2

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Theory of one-tape linear-time Turing machines

Nondeterministic one-tape off-line turing machines and their time complexity

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