Threshold circuits of bounded depth
Journal of Computer and System Sciences
Enhanced threshold gate fan-in reduction algorithms
ICYCS'93 Proceedings of the third international conference on Young computer scientists
Explicit Constructions of Depth-2 Majority Circuits for Comparison and Addition
SIAM Journal on Discrete Mathematics
On Optimal Depth Threshold Circuits for Multiplication andRelated Problems
SIAM Journal on Discrete Mathematics
Simulating Threshold Circuits by Majority Circuits
SIAM Journal on Computing
Threshold circuits of small majority-depth
Information and Computation
Signed Digit Addition and Related Operations with Threshold Logic
IEEE Transactions on Computers
Uniform constant-depth threshold circuits for division and iterated multiplication
Journal of Computer and System Sciences - Complexity 2001
On Small Depth Threshold Circuits
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
On Small Depth Threshold Circuits
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
Circuit Complexity before the Dawn of the New Millennium
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
A Linear Threshold Gate Implementation in Single Electron Technology
WVLSI '01 Proceedings of the IEEE Computer Society Workshop on VLSI 2001
Reconfigurable approximate pattern matching architectures for nanotechnology
Microelectronics Journal
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
An algorithm for nanopipelining of RTD-based circuits and architectures
IEEE Transactions on Nanotechnology
VLSI implementations of threshold logic-a comprehensive survey
IEEE Transactions on Neural Networks
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This paper obtains explicit decomposition of threshold functions into bounded fan-in threshold functions. A small fan-in is important to satisfy technology constraints for large scale integration. By employing the concept of error in the threshold function, we are able to decompose functions in LT@?"1 into a network of size O(n^c/M^2) and depth O(log^2n/logM) where n is the number of inputs of the function and M is the fan-in bound. The proposed construction enables one to trade-off the size and depth of the decomposition with the fan-in bound. Combined with the work on small weight threshold functions, this implies polynomial size, log^2 depth bounded fan-in decompositions for arbitrary threshold functions in LT"d. These results compare favorably with the classical decomposition which has a size O(2^n^-^M) and depth O(n-M). We also show that the decomposition size and depth can be significantly reduced by exploiting the relationships between the input weights. As examples of this strategy, we demonstrate an O(n^2/M) size decomposition of the majority function and, O(n/M) size decompositions of an error tolerant pattern matching function and the comparison function. In all these examples, except for the first level, all other levels use only majority functions.