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Machine-independent description of certain machine complexity classes

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Abstract

There is given one machine-independent description for a large number of classes of functions, computable on Turing machines with bounded memory and time. Let S and T be classes of nondecreasing functions, satisfying certain simple conditions. It is proved that the class of functions computable on Turing machines with memory bounded by a function from S in time bounded by a function from T coincides with the class of functions obtained from certain simple initial functions by means of explicit transformations, composition, and recursion of the form

where s\(\varepsilon \) S, t\(\varepsilon \) T, ¦x¦ is the length of the binary representation of the number x. We also get analogous descriptions of classes of functions computable with bounded memory and classes of functions computable with bounded time.

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Literature cited

  1. R. W. Ritchie, “Classes of predictably computable functions,” Trans. Am. Math. Soc.,106, 139–173 (1963).

    Google Scholar 

  2. A. Cobham, “The intrinsic computational complexity of functions,” in; Proc. 1964 International Congress of Logic, Methodology, and Philosophy of Science, Amsterdam (1965), pp. 24–30.

  3. D. B. Thompson, “Subrecursiveness; machine independent notions of computability in restricted time and storage,” Math. Syst. Theory,6, No. 1 (1972).

  4. J. C. Lind, “Computing in logarithmic space,” MAC, Cambridge, MA (1974).

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  5. B. Monein, “A recursive and grammatical characterization of the exponential time languages,” Teor. Comput. Sci.,3, 61–74 (1977).

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Authors
  1. S. V. Pakhomov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 176–184, 1979.

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Pakhomov, S.V. Machine-independent description of certain machine complexity classes. J Math Sci 20, 2358–2363 (1982). https://doi.org/10.1007/BF01629446

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  • DOI: https://doi.org/10.1007/BF01629446

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