Construction of the Multiple Processing Unit by De Bruijn Graph

De Bruijn 그래프에 의한 다중처리기 구성

  • 박춘명 (충주대학교 컴퓨터공학)
  • Published : 2006.12.30

Abstract

This paper presents a method of constructing the universal multiple processing element unit(UMPEU) by De Bruijn Graph. The second method is as following. First, we propose transformation operators in order to construct the De Bruijn UMPEU using properties of graph. Second, we construct the transformation table of De Bruijn graph using above transformation operators. Finally we construct the De Bruijn graph using transformation table. The proposed UMPEU be able to construct the De Bruijn graph for any prime number and integer value of finite fields. Also the UMPEU is applied to fault-tolerant computing system, pipeline class. parallel processing network, switching function and its circuits.

본 논문에서는 De Bruijn그래프에 기초한 다중처리기 구성 방법에 대해 논의하였다. 유한체 상의 수학적 성질과 그래프의 성질을 사용하여 변환연산자에 대해 논의하였으며, 이들 변환연산자를 이용하여 De Buijn그래프의 변환표를 도출하였다. 그리고, 이 변환표로부터 유한체 상의 De Bruijn 그래프를 도출하였다. 제안한 다중처리기는 유한체 상에서의 임의 소수와 양의 정수에 대해 구성할 수 있으며 고장허용컴퓨팅 시스템, 파이프라인 시스템, 병렬처리 네트워크, 스위칭 함수와 이의 회로, 차세대 디지털논리 시스템 및 컴퓨터 구조 등에 적 용할 수 있다.

References

  1. S. Mirta, N. R. Saxena, and E. J. McCluskey, 'Efficient Design Diversity Estimation for Combinational Circuits,' IEEE Trans. Comput. Vol.53, NO.11, pp.1493-1496, Nov. 2004 https://doi.org/10.1109/TC.2004.94
  2. V. Zyuban, D. Beutel, V. Srinivasan, M. Gschwind, P. Bose, P. N. Strenski, and P.G.Emma, 'Intergrated Analysis of Power and Oerformance for Pipelined Microprocessors,' IEEE Trans. Comput. Vol.53, NO.8, pp.1004-11016, Aug. 2004 https://doi.org/10.1109/TC.2004.46
  3. B. R. Childers and J. W. Davidson,'Custom Wide Counterflow Pipelines for high-performance Embedded Applications,' IEEE Trans. Comput. Vol.53, NO.2, pp.141-158, Feb. 2004 https://doi.org/10.1109/TC.2004.1261825
  4. F. Balarin et al., Hardware-Software Co-design of Embedded Systems: The Polis Approach, Kluwer Academic Press, Boston, June 1997
  5. R. K. Gupta, Co-Synthesis of Hardware and Software for Digital Embedded Systems, vol. 329, Kluwer Academic Publishers, Boston, Aug. 1995
  6. B.Arazi,'On the Sythesis of De-Bruijn Sequences', INFORMATION and CONTROL 49., pp.81-90, 1981 https://doi.org/10.1016/S0019-9958(81)90451-4
  7. A. Lempel, 'On a Homomorphism of the DE- Bruijn Graph and its Applications to the Design of Feedback Shift Registers', lEEE Trans. Comput. Vol.C-19, NO12, pp.1204-1209, Dec. 1970
  8. I. F. Blake, Algebraic Coding Theory : History and development, Down, Hutchinson & Ross, Inc., Stroudburg, Pennsylvania, 1973
  9. R. Lidi and G. Piltz, Applied Abstract Algebra, Spring-Verlg, Inc., 1984
  10. E. Artin, Galois Theory, NAPCO Graphic arts, Inc., Wisconsin. 1971
  11. R. Gould, Graph Theory, The Bejamin/Cummings Publishing Company, Inc., 1988
  12. M. Gondran and M. Minoux, Graph and Algorithms, A Wiley-interscience publication, Toronto, 1984