NDLI: Binary Higher Order Neural Networks for Realizing Boolean Functions

Content Provider	IEEE Xplore Digital Library
Author	Chao Zhang Jie Yang Wei Wu
Copyright Year	1990
Abstract	In order to more efficiently realize Boolean func tions by using neural networks, we propose a binary product-unit neural network (BPUNN) and a binary pi-sigma neural network (BPSNN). The network weights can be determined by one-step training. It is shown that the addition "σ," the multiplication "π" and two kinds of special weighting operations in BPUNN and BPSNN can implement the logical operators "V," "Λ," and "¬" on Boolean algebra 〈Z₂, V, Λ, ¬, 0,1〉 (Z₂ = {0,1}), respec tively. The proposed two neural networks enjoy the following advantages over the existing networks: 1) for a complete truth table of N variables with both truth and false assignments, the corresponding Boolean function can be realized by accordingly choosing a BPUNN or a BPSNN such that at most 2^N-1 hidden nodes are needed, while O(2^N), precisely 2^N or at most 2 , hidden nodes are needed by existing networks; 2) a new network BPUPS based on a collaboration of BPUNN and BPSNN can be defined to deal with incomplete truth tables, while the existing networks can only deal with complete truth tables; and 3) the values of the weights are all simply -1 or 1, while the weights of all the existing networks are real numbers. Supporting numerical experiments are provided as well. Finally, we present the risk bounds of BPUNN, BPSNN, and BPUPS, and then analyze their probably approximately correct learnability.
Sponsorship	IEEE Computational Intelligence Society
Page Count	13
File Size	472475
Starting Page	701
Ending Page	713
File Format	PDF
ISSN	10459227
Volume Number	22
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-05-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Boolean functions Artificial neural networks Neurons Approximation methods Switches Computational modeling principle disjunctive normal form Binary pi-sigma neural network binary product-unit neural network Boolean function principle conjunctive normal form
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Networks and Communications Computer Science Applications Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Realization of Boolean Functions Using Binary Pi-sigma Networks (1991)

A training algorithm for binary feedforward neural networks

Generalization in multi-layer networks of Sigma-pi units

Convergence Analysis of Batch Gradient Algorithm for Three Classes of Sigma-Pi Neural Networks

Extracting rules from trained neural networks

Mapping Boolean functions with neural networks having binary weights and zero thresholds

Application of binary neural networks for classification

A Sigma-Pi-Sigma Neural Network (SPSNN)

L/sup p/ approximation of Sigma-Pi neural networks

Binary Higher Order Neural Networks for Realizing Boolean Functions

Similar Documents

Realization of Boolean Functions Using Binary Pi-sigma Networks (1991)

A training algorithm for binary feedforward neural networks

Generalization in multi-layer networks of Sigma-pi units

Convergence Analysis of Batch Gradient Algorithm for Three Classes of Sigma-Pi Neural Networks

Extracting rules from trained neural networks

Mapping Boolean functions with neural networks having binary weights and zero thresholds

Application of binary neural networks for classification

A Sigma-Pi-Sigma Neural Network (SPSNN)

L/sup p/ approximation of Sigma-Pi neural networks

Binary Higher Order Neural Networks for Realizing Boolean Functions