Linearly Separable Boolean Function

نویسنده

  • Michael Schmitt
چکیده

The maximum absolute value of integral weights sufficient to represent any linearly separable Boolean function is investigated. It is shown that upper bounds exhibited by Muroga (1971) for rational weights satisfying the normalized System of inequalities also hold for integral weights. Therewith, the previous best known upper bound for integers is improved by approximately a factor of 1/2.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Higher Order Noise Immune Perceptrons

This paper details a systematic method for significantly enhancing the noise margins of very fast threshold gates. The method is based on adding nonlinear terms determined from the Boolean form of the linearly separable (threshold) function to be implemented. It follows that linearly separable functions can be computed with high noise immunity by higher order perceptrons. Simulation results sup...

متن کامل

Realization and bifurcation of Boolean Functions via Cellular Neural Networks

In this work, we study the realization and bifurcation of Boolean functions of four variables via a Cellular Neural Network (CNN). We characterize the basic relations between the genes and the offsets of an uncoupled CNN as well as the basis of the binary input vectors set. Based on the analysis, we have rigorously proved that there are exactly 1882 linearly separable Boolean functions of four ...

متن کامل

Implementing Universal CNN Neuron

The universal CNN neuron can realize arbitrary Boolean functions including both linearly separable Boolean functions (LSBF) and linearly not separable Boolean functions (non-LSBF). However, determining the optimal (or near-optimal) orientation vector and the parameters in the multi-nested discriminant function contained within a universal CNN neuron is still a difficult task. By the aid of the ...

متن کامل

On Specifying Boolean Functions by Labelled Examples

We say a function t in a set H of {0, 1}-valued functions defined on a set X is specified by S ⊆ X if the only function in H which agrees with t on S is t itself. The specification number of t is the least cardinality of such an S. For a general finite class of functions, we show that the specification number of any function in the class is at least equal to a parameter from [21] known as the t...

متن کامل

Using the Perceptron Algorithm to Find Consistent Hypotheses

The perceptron learning algorithm yields quite naturally an algorithm for finding a linearly separable boolean function consistent with a sample of such a function. Using the idea of a specifying sample, we give a simple proof that this algorithm is not efficient, in general. A boolean function t defined on {0, 1} is linearly separable if there are α ∈ R and θ ∈ R such that t(x) = { 1 if 〈α, x〉...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012