Article

Free access

Comparison of arithmetic functions with respect to boolean circuit depth

Author:

Helmut AltAuthors Info & Claims

STOC '84: Proceedings of the sixteenth annual ACM symposium on Theory of computing

Pages 466 - 470

https://doi.org/10.1145/800057.808714

Published: 01 December 1984 Publication History

PDF eReader

References

[1]

Aho, A.V., Hopcroft, J.E., and Ullman, J.D., The Design and Analysis of Computer Algorithms. Addison Wesley, Reading, Mass., 1974.

Digital Library

Google Scholar

[2]

Alt, H., Functions Equivalent to Integer Multiplication, ICALP 80, Noordwijkerhout, Springer Lecture Notes in Computer Science, Vol. 85, pp. 30-37, 1980.

Digital Library

Google Scholar

[3]

Alt, H., Multiplication is the Easiest Nontrivial Arithmetic Function, Proceedings 24th FOCS, Tucson, Arizona, 1983, pp. 320-322.

Digital Library

Google Scholar

[4]

Alt, H., Blum, N., On the Boolean Circuit Depth of Division Related Functions, Dept. of Computer Science, Pennsylvania State University, 1983.

Google Scholar

[5]

Brent, R.P., Fast Multiple Precision Evaluation of Elementary Functions, J. of ACM 23, pp. 242-251, 1976.

Digital Library

Google Scholar

[6]

Beame, P.W., Cook, S.A., Hoover, H.J., Small Depth Circuits for Integer Products, Powers, and Division, Dept. of Computer Science, University of Toronto, 1983

Google Scholar

[7]

Eichler, M., Einfuhrung in die Theorie der algebraischen Zahlen und Funktionen, Birkhauser Verlag, 1963.

Crossref

Google Scholar

[8]

Knuth, D.E., The Art of Computer Programming, Vol. 2, Addison Wesley, 1969

Digital Library

Google Scholar

[9]

Ofman, Y., On the Algorithmic Complexity of Discrete Functions, Sov. Phys. Dokl., Vol. 7.7, 1963, pp. 589-591

Google Scholar

[10]

Reif, J., Logarithmic Depth Circuits for Algebraic Functions, Proc. 24th Annual FOCS, Tucson, AR, 1983, pp. 138-145

Google Scholar

[11]

Savage, J., The Complexity of Computing, J. Wiley and Sons, N.Y., 1976

Digital Library

Google Scholar

Cited By

View all

Braverman MRojas CSchneider J(2018)Tight space-noise tradeoffs in computing the ergodic measureSbornik: Mathematics10.1070/SM8884208:12(1758-1783)Online publication date: 19-Feb-2018
https://doi.org/10.1070/SM8884
Okabe YTakagi NYajima S(2007)Log‐depth circuits for elementary functions using residue number systemElectronics and Communications in Japan (Part III: Fundamental Electronic Science)10.1002/ecjc.443074080474:8(31-38)Online publication date: 21-Feb-2007
https://doi.org/10.1002/ecjc.4430740804
Ahrendt T(1999)Fast computations of the exponential functionProceedings of the 16th annual conference on Theoretical aspects of computer science10.5555/1764891.1764930(302-312)Online publication date: 4-Mar-1999
https://dl.acm.org/doi/10.5555/1764891.1764930
Show More Cited By

Index Terms

Comparison of arithmetic functions with respect to boolean circuit depth

Recommendations

Evolutionary Synthesis of Arithmetic Circuit Structures

This paper presents an efficient graph-based evolutionary optimization technique called Evolutionary Graph Generation (EGG), and its application to arithmetic circuit synthesis. Key features of EGG are to employ a graph-based representation of ...
The complexity of depth-3 circuits computing symmetric Boolean functions

We give tight lower bounds for the size of depth-3 circuits with limited bottom fanin computing symmetric Boolean functions. We show that any depth-3 circuit with bottom fanin k which computes the Boolean function Exact_n/(k+1)ⁿ, has at least (1 + 1/k)ⁿ/(...
Evolutionary synthesis of arithmetic circuit structures
Artificial intelligence in logic design

This paper presents an efficient graph-based evolutionary optimization technique called Evolutionary Graph Generation (EGG), and its application to arithmetic circuit synthesis. Key features of EGG are to employ a graph-based representation of ...

Comments

Information & Contributors

Information

Published In

STOC '84: Proceedings of the sixteenth annual ACM symposium on Theory of computing

December 1984

547 pages

ISBN:0897911334

DOI:10.1145/800057

Chairman:
Richard DeMillo

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 1984

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Acceptance Rates

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

7
Total Citations
View Citations
812
Total Downloads

Downloads (Last 12 months)97
Downloads (Last 6 weeks)13

Reflects downloads up to 12 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Braverman MRojas CSchneider J(2018)Tight space-noise tradeoffs in computing the ergodic measureSbornik: Mathematics10.1070/SM8884208:12(1758-1783)Online publication date: 19-Feb-2018
https://doi.org/10.1070/SM8884
Okabe YTakagi NYajima S(2007)Log‐depth circuits for elementary functions using residue number systemElectronics and Communications in Japan (Part III: Fundamental Electronic Science)10.1002/ecjc.443074080474:8(31-38)Online publication date: 21-Feb-2007
https://doi.org/10.1002/ecjc.4430740804
Ahrendt T(1999)Fast computations of the exponential functionProceedings of the 16th annual conference on Theoretical aspects of computer science10.5555/1764891.1764930(302-312)Online publication date: 4-Mar-1999
https://dl.acm.org/doi/10.5555/1764891.1764930
Fich FTompa MSedgewick R(1985)The parallel complexity of exponentiating polynomials over finite fieldsProceedings of the seventeenth annual ACM symposium on Theory of computing10.1145/22145.22150(38-47)Online publication date: 1-Dec-1985
https://dl.acm.org/doi/10.1145/22145.22150
Jung H(1985)Depth efficient transformations of arithmetic into boolean circuitsFundamentals of Computation Theory10.1007/BFb0028801(167-174)Online publication date: 1985
https://doi.org/10.1007/BFb0028801
von zur Gathen J(1984)Parallel PoweringProceedings of the 25th Annual Symposium onFoundations of Computer Science, 198410.1109/SFCS.1984.715898(31-36)Online publication date: 24-Oct-1984
https://dl.acm.org/doi/10.1109/SFCS.1984.715898
Beame PCook SHoover H(1984)Log Depth Circuits For Division And Related ProblemsProceedings of the 25th Annual Symposium onFoundations of Computer Science, 198410.1109/SFCS.1984.715894(1-6)Online publication date: 24-Oct-1984
https://dl.acm.org/doi/10.1109/SFCS.1984.715894

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

References

Cited By

Index Terms

Recommendations

Evolutionary Synthesis of Arithmetic Circuit Structures

The complexity of depth-3 circuits computing symmetric Boolean functions

Evolutionary synthesis of arithmetic circuit structures

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Acceptance Rates

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations