Skip to main content
SpringerLink
Log in

Possibility of maximum paralleling of problems on associative processors

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

A computational model of associative type is proposed. For it a program is written which does not contain loops and has the following properties. The program's original data are a normal algorithmA (its notation) and a worda, while the results are a Boolean value

and a wordR. IfA is applicable to worda, then we can indicate a finite memory such that the program, having worked on this memory, yields the valuetrue as

andA(a) asR. However, ifA is not applicable toa, then the program does not work on any (finite) memory and always yields the valuefalse as

, If the program works on an infinite memory, then after its work

takes the valuetrue if and only ifA is applicable toa; moreover, in the case of applicabilityR takes the valueA(a). The present paper contains a more detailed exposition of the result published in Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk USSR,70 (1977).

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. A. N. Myamlin and A. A. Sosnin, “Supercomputers: architecture and areas of application,” Preprint, No. 15, Inst. Prikl. Mat., Moscow (1977).

    Google Scholar 

  2. D. H. Enslow (ed.), Multiprocessors and Parallel Processing, Wiley, New York (1974).

    Google Scholar 

  3. I. V. Prangishvili (ed.), Homogeneous Microelectronic Associative Processors [in Russian], Moscow (1973).

  4. Ya. I. Fet, Mass Processing of Information in Specialized Homogeneous Processors [in Russian], Novosibirsk (1976).

  5. A. S. Narin'yani, “Theory of parallel programming. Formal models. I,” Kibernetika, No. 3, 1–15 (1974).

    Google Scholar 

  6. A. S. Narin'yani, “Theory of parallel programming. Formal models. II,” Kibernetika, No. 5, 1–14 (1974).

    Google Scholar 

  7. M. S. Burgin and A. Yu. Karasik, “Analysis of one abstract model of computing systems,” Programmirovanie, No. 1, 72–82 (1975).

    Google Scholar 

  8. M. S. Burgin and A. Yu. Karasik, “Operators of a multidimensional structure-oriented parallel-processing model,” Avtomat. Telemekh., No. 8, 179–185 (1976).

    Google Scholar 

  9. G. M. Popova and I. V. Prangishvili, “Associative parallel processor for group processing of data,” Avtomat. Telemekh., No. 1, 171–184 (1972).

    Google Scholar 

  10. V. N. Aleeva and Ya. I. Fet, “Associative processor for large-block processing of information. Optimization,” Sb. Tr. Inst. Mat. Sib. Otd. Akad. Nauk SSSR, No. 15(32), 154–177 (1974).

    Google Scholar 

  11. Y. Chu, Computer Organization and Microprogramming, Prentice-Hall, Englewood Cliffs, New Jersey (1972).

    Google Scholar 

  12. M. M. Lebedinskii, “On the possibilities of carrying out parallel processing on a three-dimensional associative parallel processor,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,70, 140–160 (1977).

    Google Scholar 

Download references

Authors
  1. M. M. Lebedinskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from, Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 90, pp. 83–149, 1979.

In conclusion, the author thanks K. V. Shakhbazyan for constant attention to the work.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lebedinskii, M.M. Possibility of maximum paralleling of problems on associative processors. J Math Sci 20, 1959–2011 (1982). https://doi.org/10.1007/BF01680566

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01680566

Keywords

Search

Navigation