research-article

A Computer Algorithm for Minimizing Reed-Muller Canonical Forms

Authors:

H. Fleisher,

M. Tavel,

J. YeagerAuthors Info & Claims

IEEE Transactions on Computers, Volume 36, Issue 2

Pages 247 - 250

https://doi.org/10.1109/TC.1987.1676890

Published: 01 February 1987 Publication History

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Abstract

A computer algorithm is presented that uses geometrical operations to minimize multioutput Reed-Muller expansions of up to ten variables.

References

[1]

For a recent analytic approach and additional references see J. P. Robinson and C.-L. Yeh, "A method for modulo-2 minimization" IEEE Trans. Comput., vol. C-31, pp. 800-801, Aug. 1982.

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[2]

X. Wu, X. Chen, and S. L. Hurst, "Mapping of Reed-Muller coefficients and the minimisation of Exclusive-OR switching functions," Proc. IEE, part E, vol. 129, pp. 15-20, Jan. 1982.

Google Scholar

[3]

H. Fleisher, M. Tavel, and J. Yeager, "Exclusive-OR representations of Boolean functions," IBM J. Res. Develop., vol. 27, pp. 412-416, July 1983.

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Google Scholar

[4]

P. Roth, Computer Logic, Testing and Verification, Rockville, MD: Computer Science, 1980, p. 6.

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Cited By

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Mizuki TTsubata HNishizeki T(2009)Minimizing AND-EXOR Expressions for Multiple-Valued Two-Input Logic FunctionsProceedings of the 6th Annual Conference on Theory and Applications of Models of Computation10.1007/978-3-642-02017-9_33(301-310)Online publication date: 12-May-2009
https://dl.acm.org/doi/10.1007/978-3-642-02017-9_33
Mizuki TOtagiri TSone H(2006)Secure computations in a minimal model using multiple-valued ESOP expressionsProceedings of the Third international conference on Theory and Applications of Models of Computation10.1007/11750321_52(547-554)Online publication date: 15-May-2006
https://dl.acm.org/doi/10.1007/11750321_52
Ye YRoy KYoffa EDe Micheli GRabaey J(1997)A graph-based synthesis algorithm for AND/XOR networksProceedings of the 34th annual Design Automation Conference10.1145/266021.266044(107-112)Online publication date: 13-Jun-1997
https://dl.acm.org/doi/10.1145/266021.266044
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Index Terms

A Computer Algorithm for Minimizing Reed-Muller Canonical Forms
1. Hardware
  1. Integrated circuits
    1. Logic circuits
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image IEEE Transactions on Computers

IEEE Transactions on Computers Volume 36, Issue 2

February 1987

135 pages

ISSN:0018-9340

Editor:
Bruce D. Shriver

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IEEE Computer Society

United States

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Published: 01 February 1987

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Mizuki TTsubata HNishizeki T(2009)Minimizing AND-EXOR Expressions for Multiple-Valued Two-Input Logic FunctionsProceedings of the 6th Annual Conference on Theory and Applications of Models of Computation10.1007/978-3-642-02017-9_33(301-310)Online publication date: 12-May-2009
https://dl.acm.org/doi/10.1007/978-3-642-02017-9_33
Mizuki TOtagiri TSone H(2006)Secure computations in a minimal model using multiple-valued ESOP expressionsProceedings of the Third international conference on Theory and Applications of Models of Computation10.1007/11750321_52(547-554)Online publication date: 15-May-2006
https://dl.acm.org/doi/10.1007/11750321_52
Ye YRoy KYoffa EDe Micheli GRabaey J(1997)A graph-based synthesis algorithm for AND/XOR networksProceedings of the 34th annual Design Automation Conference10.1145/266021.266044(107-112)Online publication date: 13-Jun-1997
https://dl.acm.org/doi/10.1145/266021.266044
Sasao TBesslich P(1990)On the Complexity of Mod-2l Sum PLA'sIEEE Transactions on Computers10.1109/12.4521239:2(262-266)Online publication date: 1-Feb-1990
https://dl.acm.org/doi/10.1109/12.45212
Helliwell MPerkowski MShaklee DNewton A(1988)A fast algorithm to minimize multi-output mixed-polarity generalized Reed-Muller formsProceedings of the 25th ACM/IEEE Design Automation Conference10.5555/285730.285799(427-432)Online publication date: 1-Jun-1988
https://dl.acm.org/doi/10.5555/285730.285799

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Recommendations

Easily Testable Realizations for Generalized Reed-Muller Expressions

Evaluation of m-Valued Fixed Polarity Generalizations of Reed-Muller Canonical Form

Reed-Muller Canonical Forms in Multivalued Logic

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