ENHANCED THRESHOLD GATE FAN-IN REDUCTION ALGORITHMS 1

The paper describes and improves on a Boolean neural network (NN) fan-in reduction algorithm, with a view to possible VLSI implementation of NNs using threshold gates (TGs). Constructive proofs are given for: (i) at least halving the size; (ii) reducing the depth from O(N) to O(logN). Lastly a fresh algorithm which reduces the size to polynomial is suggested.

[1]  Robert C. Minnick,et al.  Linear-Input Logic , 1961, IRE Trans. Electron. Comput..

[2]  N. P. Red’kin Synthesis of threshold circuits for certain classes of Boolean functions , 1970 .

[3]  Robert O. Winder,et al.  Threshold logic , 1971, IEEE Spectrum.

[4]  Saburo Muroga,et al.  Threshold logic and its applications , 1971 .

[5]  M. V. Wilkes,et al.  The Art of Computer Programming, Volume 3, Sorting and Searching , 1974 .

[6]  N. Biswas,et al.  Testing threshold functions using implied minterm structure , 1983 .

[7]  Thompson The VLSI Complexity of Sorting , 1983, IEEE Transactions on Computers.

[8]  Leon E. Winslow,et al.  The Analysis and Design of Some New Sorting Machines , 1983, IEEE Transactions on Computers.

[9]  Larry Rudolph,et al.  A Robust Sorting Network , 1985, IEEE Transactions on Computers.

[10]  Frank Thomson Leighton,et al.  Tight Bounds on the Complexity of Parallel Sorting , 1984, IEEE Transactions on Computers.

[11]  Alan R. Siegel,et al.  Minimum Storage Sorting Networks , 1985, IEEE Transactions on Computers.

[12]  Tom Baker,et al.  Modifications to artificial neural networks models for Digital Hardware Implementation , 1988 .

[13]  Jehoshua Bruck,et al.  Neural computation of arithmetic functions , 1990 .

[14]  Jehoshua Bruck,et al.  Harmonic Analysis of Polynomial Threshold Functions , 1990, SIAM J. Discret. Math..

[15]  Yoshiyasu Takefuji,et al.  A super-parallel sorting algorithm based on neural networks , 1990 .

[16]  Thomas Kailath,et al.  Depth-Size Tradeoffs for Neural Computation , 1991, IEEE Trans. Computers.

[17]  Eddy Mayoraz,et al.  On the Power of Networks of Majority Functions , 1991, IWANN.

[18]  Rudy Lauwereins,et al.  Efficient implementation of a neural multiplier , 1991 .

[19]  T. Kailath,et al.  Computing With Almost Optimal Size Threshold Circuits , 1991, Proceedings. 1991 IEEE International Symposium on Information Theory.

[20]  Cesare Alippi,et al.  Hardware requirements to digital VLSI implementation of neural networks , 1991, [Proceedings] 1991 IEEE International Joint Conference on Neural Networks.

[21]  N. H. Biswas,et al.  IMS algorithm for learning representations in Boolean neural networks , 1991, [Proceedings] 1991 IEEE International Joint Conference on Neural Networks.

[22]  Jehoshua Bruck,et al.  On the Power of Threshold Circuits with Small Weights , 1991, SIAM J. Discret. Math..

[23]  Thomas Hofmeister,et al.  Some Notes on Threshold Circuits, and Multiplication in Depth 4 , 1991, Inf. Process. Lett..

[24]  R. Lauwereins,et al.  Using Threshold Gates To Implement Sigmoid Nonlinearity , 1992 .

[25]  Rudy Lauwereins,et al.  Simpler Neural Networks by Fan-In Reduction , 1992 .

[26]  Jehoshua Bruck,et al.  Polynomial threshold functions, AC functions and spectrum norms , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[27]  Rudy Lauwereins,et al.  Efficient decomposition of comparison and its applications , 1993, ESANN.

[28]  Yuzo Hirai,et al.  Hardware implementation of neural networks in Japan , 1993, Neurocomputing.

[29]  Jehoshua Bruck,et al.  Depth efficient neural networks for division and related problems , 1993, IEEE Trans. Inf. Theory.

[30]  Noga Alon,et al.  Explicit Constructions of Depth-2 Majority Circuits for Comparison and Addition , 1994, SIAM J. Discret. Math..