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

Katedra Systemów Cyfrowych (RAU/RAU12)

United Technologies Corporation

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7 Cytowania z bazy Scopus

Abstrakt

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.

Język oryginału	angielski
Tytuł publikacji goszczącej	Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010
Strony	293-296
Liczba stron	4
Identyfikatory DOI	https://doi.org/10.1109/DDECS.2010.5491764
Status publikacji	Opublikowano - 2010
Wydarzenie	13th IEEE International Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010 - Vienna, Austria Czas trwania: 14 kwi 2010 → 16 kwi 2010

Seria publikacji

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

Konferencja

Konferencja	13th IEEE International Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010
Kraj/Terytorium	Austria
Miejscowość	Vienna
Okres	14/04/10 → 16/04/10

Obszary tematyczne ASJC Scopus

Sprzęt i architektura
Inżynieria elektryczna i elektroniczna

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10.1109/DDECS.2010.5491764

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Cytowanie

Hrynkiewicz, E., & Kołodziński, S. (2010). Non-disjoint decomposition of logic functions in Reed-Muller spectral domain. W Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010 (str. 293-296). Artykułu 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. str. 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. w 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, str. 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. str. 293-296 5491764 (Proceedings of the 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2010).

Wyniki badań: Rozdział w książce/raport/materiał konferencyjny › Wkład w konferencję › recenzja

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

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

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Obszary tematyczne ASJC Scopus

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