Non-disjoint decomposition of logic functions in Reed-Muller spectral domain

Edward Hrynkiewicz; Stefan Kołodziński

doi:10.1109/DDECS.2010.5491764

Non-disjoint decomposition of logic functions in Reed-Muller spectral domain

Edward Hrynkiewicz
, Stefan Kołodziński

Department of Digital Systems (RAU/RAU12)

United Technologies Corporation

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Citations (Scopus)

Abstract

The paper deals with the problems of input variables assigning to the free set bounded set and common set during logic function non-disjoint decomposition. The Ashenhurst and Curtis decompositions are considered with respect to implementation of logic functions in LUT based FPGA. The method of finding profitable common variables set (from the point of view of non-disjoint decomposition) is based on utilization of Logic Differential Calculus and authors experiences. The decomposition is carried out in Reed-Muller spectral domain because the Boolean differentials are easy calculated from Reed-Muller form of logic function which is obtained as reverse Reed-Muller transform. The results of decomposition are very promising.

Original language	English
Title of host publication	Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010
Pages	293-296
Number of pages	4
DOIs	https://doi.org/10.1109/DDECS.2010.5491764
Publication status	Published - 2010
Event	13th IEEE International Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010 - Vienna, Austria Duration: 14 Apr 2010 → 16 Apr 2010

Publication series

Name	Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010

Conference

Conference	13th IEEE International Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010
Country/Territory	Austria
City	Vienna
Period	14/04/10 → 16/04/10

Keywords

Boolean Differential Calculus
FPGA
Non-disjoint decomposition
Reed-Muller spectrum

ASJC Scopus subject areas

Hardware and Architecture
Electrical and Electronic Engineering

Access to Document

10.1109/DDECS.2010.5491764

Cite this

Hrynkiewicz, E., & Kołodziński, S. (2010). Non-disjoint decomposition of logic functions in Reed-Muller spectral domain. In Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010 (pp. 293-296). Article 5491764 (Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010). https://doi.org/10.1109/DDECS.2010.5491764

Hrynkiewicz, Edward ; Kołodziński, Stefan. / Non-disjoint decomposition of logic functions in Reed-Muller spectral domain. Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010. 2010. pp. 293-296 (Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010).

@inproceedings{47fd17e3a73c464593131ca64e889e77,

title = "Non-disjoint decomposition of logic functions in Reed-Muller spectral domain",

abstract = "The paper deals with the problems of input variables assigning to the free set bounded set and common set during logic function non-disjoint decomposition. The Ashenhurst and Curtis decompositions are considered with respect to implementation of logic functions in LUT based FPGA. The method of finding profitable common variables set (from the point of view of non-disjoint decomposition) is based on utilization of Logic Differential Calculus and authors experiences. The decomposition is carried out in Reed-Muller spectral domain because the Boolean differentials are easy calculated from Reed-Muller form of logic function which is obtained as reverse Reed-Muller transform. The results of decomposition are very promising.",

keywords = "Boolean Differential Calculus, FPGA, Non-disjoint decomposition, Reed-Muller spectrum",

author = "Edward Hrynkiewicz and Stefan Ko{\l}odzi{\'n}ski",

year = "2010",

doi = "10.1109/DDECS.2010.5491764",

language = "English",

isbn = "9781424466139",

series = "Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010",

pages = "293--296",

booktitle = "Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010",

note = "13th IEEE International Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010 ; Conference date: 14-04-2010 Through 16-04-2010",

}

Hrynkiewicz, E & Kołodziński, S 2010, Non-disjoint decomposition of logic functions in Reed-Muller spectral domain. in Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010., 5491764, Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010, pp. 293-296, 13th IEEE International Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010, Vienna, Austria, 14/04/10. https://doi.org/10.1109/DDECS.2010.5491764

Non-disjoint decomposition of logic functions in Reed-Muller spectral domain. / Hrynkiewicz, Edward; Kołodziński, Stefan.
Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010. 2010. p. 293-296 5491764 (Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Non-disjoint decomposition of logic functions in Reed-Muller spectral domain

AU - Hrynkiewicz, Edward

AU - Kołodziński, Stefan

PY - 2010

Y1 - 2010

N2 - The paper deals with the problems of input variables assigning to the free set bounded set and common set during logic function non-disjoint decomposition. The Ashenhurst and Curtis decompositions are considered with respect to implementation of logic functions in LUT based FPGA. The method of finding profitable common variables set (from the point of view of non-disjoint decomposition) is based on utilization of Logic Differential Calculus and authors experiences. The decomposition is carried out in Reed-Muller spectral domain because the Boolean differentials are easy calculated from Reed-Muller form of logic function which is obtained as reverse Reed-Muller transform. The results of decomposition are very promising.

AB - The paper deals with the problems of input variables assigning to the free set bounded set and common set during logic function non-disjoint decomposition. The Ashenhurst and Curtis decompositions are considered with respect to implementation of logic functions in LUT based FPGA. The method of finding profitable common variables set (from the point of view of non-disjoint decomposition) is based on utilization of Logic Differential Calculus and authors experiences. The decomposition is carried out in Reed-Muller spectral domain because the Boolean differentials are easy calculated from Reed-Muller form of logic function which is obtained as reverse Reed-Muller transform. The results of decomposition are very promising.

KW - Boolean Differential Calculus

KW - FPGA

KW - Non-disjoint decomposition

KW - Reed-Muller spectrum

UR - https://www.scopus.com/pages/publications/77954912798

U2 - 10.1109/DDECS.2010.5491764

DO - 10.1109/DDECS.2010.5491764

M3 - Conference contribution

AN - SCOPUS:77954912798

SN - 9781424466139

T3 - Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010

SP - 293

EP - 296

BT - Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010

T2 - 13th IEEE International Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010

Y2 - 14 April 2010 through 16 April 2010

ER -

Hrynkiewicz E, Kołodziński S. Non-disjoint decomposition of logic functions in Reed-Muller spectral domain. In Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010. 2010. p. 293-296. 5491764. (Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010). doi: 10.1109/DDECS.2010.5491764

Non-disjoint decomposition of logic functions in Reed-Muller spectral domain

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this