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 IEEE International Workshop on Cellular Neural Networks and their Applications
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages323-338
Number of pages16
Volume2002-January
ISBN (Print)981238121X
DOIs
Publication statusPublished - 2002
Event7th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2002 - Frankfurt, Germany
Duration: Jul 22 2002Jul 24 2002

Other

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

Fingerprint

Computational complexity
Computational Complexity
Cellular arrays
Recursive functions
Recursive Functions
Computer Architecture
Computer architecture
Complexity Theory
Computing
Biology
Dissipation
Energy dissipation
Reasoning
Paradigm
Logic
Integer
Relevance

Keywords

  • Biology computing
  • Cellular neural networks
  • CMOS technology
  • 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

Cite this

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

Computational and computer complexity of analogic cellular wave computers. / Roska, T.

Proceedings of the IEEE International Workshop on Cellular Neural Networks and their Applications. Vol. 2002-January Institute of Electrical and Electronics Engineers Inc., 2002. p. 323-338 1035067.

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

Roska, T 2002, Computational and computer complexity of analogic cellular wave computers. in Proceedings of the IEEE International Workshop on Cellular Neural Networks and their Applications. vol. 2002-January, 1035067, Institute of Electrical and Electronics Engineers Inc., pp. 323-338, 7th IEEE International Workshop on Cellular Neural Networks and their Applications, CNNA 2002, Frankfurt, Germany, 7/22/02. https://doi.org/10.1109/CNNA.2002.1035067
Roska T. Computational and computer complexity of analogic cellular wave computers. In Proceedings of the IEEE International Workshop on Cellular Neural Networks and their Applications. Vol. 2002-January. Institute of Electrical and Electronics Engineers Inc. 2002. p. 323-338. 1035067 https://doi.org/10.1109/CNNA.2002.1035067
Roska, T. / Computational and computer complexity of analogic cellular wave computers. Proceedings of the IEEE International Workshop on Cellular Neural Networks and their Applications. Vol. 2002-January Institute of Electrical and Electronics Engineers Inc., 2002. pp. 323-338
@inproceedings{ceb33af28a6b4bed984274beb5618724,
title = "Computational and computer complexity of analogic cellular wave computers",
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.",
keywords = "Biology computing, Cellular neural networks, CMOS technology, Computational complexity, Computer aided instruction, Computer architecture, Optical arrays, Optical computing, Physics computing, Turing machines",
author = "T. Roska",
year = "2002",
doi = "10.1109/CNNA.2002.1035067",
language = "English",
isbn = "981238121X",
volume = "2002-January",
pages = "323--338",
booktitle = "Proceedings of the IEEE International Workshop on Cellular Neural Networks and their Applications",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - GEN

T1 - Computational and computer complexity of analogic cellular wave computers

AU - Roska, T.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - Biology computing

KW - Cellular neural networks

KW - CMOS technology

KW - Computational complexity

KW - Computer aided instruction

KW - Computer architecture

KW - Optical arrays

KW - Optical computing

KW - Physics computing

KW - Turing machines

UR - http://www.scopus.com/inward/record.url?scp=84914692639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84914692639&partnerID=8YFLogxK

U2 - 10.1109/CNNA.2002.1035067

DO - 10.1109/CNNA.2002.1035067

M3 - Conference contribution

AN - SCOPUS:84914692639

SN - 981238121X

VL - 2002-January

SP - 323

EP - 338

BT - Proceedings of the IEEE International Workshop on Cellular Neural Networks and their Applications

PB - Institute of Electrical and Electronics Engineers Inc.

ER -