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Abstract:
We introduce a new Boolean computing element related to the
Linear Threshold element, which is the Boolean version of the
neuron. Instead of the sign function, it computes an arbitrary
(with polynomialy many transitions) Boolean function of the
weighted sum of its inputs. We call the new computing element an
LTM element, which stands for Linear Threshold with Multiple
transitions.
The paper consists of the following main contributions related to
our study of LTM circuits: (i) the creation of efficient designs of
LTM circuits for the addition of a multiple number of integers and
the product of two integers. In particular, we show how to compute
the addition of m integers with a single layer of LTM elements.
(ii) a proof that the area of the VLSI layout is reduced from
O(n
2
)
in LT circuits to
O(n)
in LTM circuits, for
n
inputs symmetric Boolean functions, and (iii) the characterization
of the computing power of LTM relative to LT circuits.
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