Computational and computer complexity of analogic cellular wave computers

Research output: Chapter in Book/Report/Conference proceedingConference contribution

19 Citations (Scopus)

Abstract

Computational complexity and computer complexity issues are studied in different architectural settings. Three mathematical machines are considered: the universal machine on integers (UMZ), the universal machine on reals (UMR) and the universal machine on flows (UMF). The three machines induce different kinds of computational difficulties: combinatorial, algebraic, and dynamic, respectively. After a broader overview of computational complexity issues, it is shown, following the reasoning related the UMR, that in many cases the size is not the most important parameter related to computational complexity. Emerging new computing and computer architectures as well as their physical implementation suggest a new look at computational and computer complexities. The new analogic cellular array computer paradigm based on the CNN Universal Machine (generalized to UMF), and its physical implementation in CMOS and optical technologies, proves experimentally the relevance of the role of accuracy and problem parameter role in computational complexity, as well as the need of rigorous definition of computational complexity for UMF. It is also shown that choosing the spatial temporal elementary instructions, as well as taking into account the area and power dissipation, these choices inherently influence computational complexity and computer complexity, respectively. Comments related to biology relevance of the UMF are presented in relation to complexity theory. It is shown that algorithms using spatial-temporal continuous elementary instructions (a-recursive functions) represent not only a new world in computing, but also a more general type of logic inferencing.

Original languageEnglish
Title of host publicationProceedings of the 7th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2002
EditorsRonald Tetzlaff
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages323-338
Number of pages16
ISBN (Electronic)981238121X
DOIs
Publication statusPublished - Jan 1 2002
Event7th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2002 - Frankfurt, Germany
Duration: Jul 22 2002Jul 24 2002

Publication series

NameProceedings of the IEEE International Workshop on Cellular Neural Networks and their Applications
Volume2002-January

Other

Other7th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2002
CountryGermany
CityFrankfurt
Period7/22/027/24/02

Keywords

  • Biology computing
  • CMOS technology
  • Cellular neural networks
  • Computational complexity
  • Computer aided instruction
  • Computer architecture
  • Optical arrays
  • Optical computing
  • Physics computing
  • Turing machines

ASJC Scopus subject areas

  • Hardware and Architecture
  • Software
  • Electrical and Electronic Engineering
  • Modelling and Simulation

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  • Cite this

    Roska, T. (2002). Computational and computer complexity of analogic cellular wave computers. In R. Tetzlaff (Ed.), Proceedings of the 7th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2002 (pp. 323-338). [1035067] (Proceedings of the IEEE International Workshop on Cellular Neural Networks and their Applications; Vol. 2002-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CNNA.2002.1035067