Skip to main content

Storage modification machines

  • Hauptvorträge
  • Conference paper
  • First Online:
Theoretical Computer Science 4th GI Conference

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 67))

Abstract

In 1970 the author introduced a new machine model (cf. [11]) now called storage modification machine (SMM) and posed the intuitive thesis that (among all models of an atomistic nature) this model possesses extreme flexibility. In the meantime some progress has been made in comparing SMMs with other machine models by investigating the possibility of real time reductions. Here we give a survey of our present knowledge of SMMs.

We briefly explain the notion of Δ-structures (which serve as storage devices), the instruction set of an SMM, the related successor RAM model and its real time equivalence to the SMM model. Then we discuss the relationship between SMMs and Kolmogorov Uspenskii machines (KUM) introduced in [7]. In spite of the obvious similarities KUMs are different from SMMs; they are certainly not stronger but perhaps weaker than SMMs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References.

  1. A.V. Aho, J.E. Hopcroft and J.D. Ullman, The Design and Analysis of Computer Algorithms (Addison-Wesley, Reading, MA, 1974).

    Google Scholar 

  2. A. Church, An Unsolvable Problem of Elementary Number Theory, Amer. J. Math. 58 (1936) 345–363.

    Google Scholar 

  3. D.Yu. Grigoryev, Kolmogorov algorithms are stronger than Turing machines, in: Matijasevič, Slisenko, eds., Investigations in constructive mathematics and mathematical logic VII (Russian; Izdat. Nauka, Leningrad, 1976) 29–37.

    Google Scholar 

  4. J.E. Hopcroft, W.J. Paul and L.G. Valiant, On time versus space and related problems, Proc. 16th Ann. IEEE Symp. Foundations Comp. Sci., Berkeley (1975) 57–64.

    Google Scholar 

  5. D.E. Knuth, The Art of Computer Programming vol. 2, Seminumerical Algorithms (2nd ed., Addison-Wesley, Reading, MA, 1971)

    Google Scholar 

  6. D.E. Knuth, The Art of Computer Programming, vol. 3, Sorting and Searching (Addison-Wesley, Reading, MA, 1973).

    Google Scholar 

  7. A.N. Kolmogorov and V.A. Uspenskii, On the definition of an algorithm, Uspehi Mat. Nauk 13 (1958) 3–28; AMS Transl. 2nd ser. vol. 29 (1963) 217–245.

    Google Scholar 

  8. M.V. Kubinec, Recognition of the self-intersection of a plane trajectory by Kolmogorov's algorithm, in: Matijasevič, Slisenko, eds., Investigations in constructive mathematics and mathematical logic V (Russian; Izdat. Nauka, Leningrad, 1972) 35–44.

    Google Scholar 

  9. W.J. Paul, Komplexitätstheorie (Teubner, Stuttgart, 1978).

    Google Scholar 

  10. C.P. Schnorr, Rekursive Funktionen und ihre Komplexität (Teubner, Stuttgart, 1974).

    Google Scholar 

  11. A. Schönhage, Universelle Turing Speicherung, in: Dörr, Hotz, eds., Automatentheorie und Formale Sprachen (Bibliogr. Institut, Mannheim, 1970) 369–383.

    Google Scholar 

  12. A. Schönhage, Real-time simulation of multidimensional Turing machines by storage modification machines, Technical Memorandum 37, M.I.T. Project MAC, Cambridge, MA (1973).

    Google Scholar 

  13. A. Schönhage and V. Strassen, Schnelle Multiplikation großer Zahlen, Computing 7 (1971) 281–292.

    Google Scholar 

Download references

Authors

Editor information

K. Weihrauch

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Schönhage, A. (1979). Storage modification machines. In: Weihrauch, K. (eds) Theoretical Computer Science 4th GI Conference. Lecture Notes in Computer Science, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09118-1_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-09118-1_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09118-9

  • Online ISBN: 978-3-540-35517-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics