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Zap. Nauchn. Sem. LOMI, 1979, Volume 88, Pages 176–185 (Mi znsl3111)  

Machine-independent description of some machine complexity classes

S. V. Pakhomov


Abstract: A uniform machine-independent description is given for a large number of classes of functions computable by Turing machines within, bounded space and time. Let $S$ and $T$ be the classes of nondecreasing functions satisfying conditions (S1)–(S3), (T1), (T2), (ST1)–(ST3). It is proved that the class of functions computable by a Turing machine within space bounded by a function belonging to $S$ and within time bounded by a function belonging to $T$ is equal to the class of functions obtainable from some simple initial functions by means of explicit transformation, substitution and recursion of the type ($*$) where $s\in S$, $t\in T$. Analogous descriptions of classes of functions computable within bounded space and classes of functions computable within bounded time are also presented.

Full text: PDF file (497 kB)

English version:
Journal of Soviet Mathematics, 1982, 20:4, 2358–2363

Bibliographic databases:

UDC: 510.52

Citation: S. V. Pakhomov, “Machine-independent description of some machine complexity classes”, Studies in constructive mathematics and mathematical logic. Part VIII, Zap. Nauchn. Sem. LOMI, 88, "Nauka", Leningrad. Otdel., Leningrad, 1979, 176–185; J. Soviet Math., 20:4 (1982), 2358–2363

Citation in format AMSBIB
\Bibitem{Pak79}
\by S.~V.~Pakhomov
\paper Machine-independent description of some machine complexity classes
\inbook Studies in constructive mathematics and mathematical logic. Part~VIII
\serial Zap. Nauchn. Sem. LOMI
\yr 1979
\vol 88
\pages 176--185
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl3111}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=556228}
\zmath{https://zbmath.org/?q=an:0429.03019|0493.03014}
\transl
\jour J. Soviet Math.
\yr 1982
\vol 20
\issue 4
\pages 2358--2363
\crossref{https://doi.org/10.1007/BF01629446}


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