Showing papers by "Alon Orlitsky published in 1995"
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TL;DR: It is shown that if only the sender can transmit, the number of bits required is a conditional entropy of a naturally defined graph.
Abstract: A sender communicates with a receiver who wishes to reliably evaluate a function of their combined data. We show that if only the sender can transmit, the number of bits required is a conditional entropy of a naturally defined graph. We also determine the number of bits needed when the communicators exchange two messages. Reference is made to the results of rate distortion in evaluating the function of two random variables.
455 citations
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TL;DR: It is shown that if only the sender can transmit, the number of bits required is a conditional entropy of a naturally defined graph.
Abstract: A sender communicates with a receiver who wishes to reliably evaluate a function of their combined data. We show that if only the sender can transmit, the number of bits required is a conditional entropy of a naturally defined graph. We also determine the number of bits needed when the communicators exchange two messages.
280 citations
TL;DR: Viewing n-variable Boolean functions as vectors in R 2n, basic tools from linear algebra and linear programming are invoked to derive new results on the realizability of Boolean functions using threshold gates to obtain lower bound on the number of input functions required by a threshold gate implementing a given function.
Abstract: Viewing n-variable Boolean functions as vectors in R 2n, we invoke basic tools from linear algebra and linear programming to derive new results on the realizability of Boolean functions using threshold gates. Using this approach, we obtain: (1) a lower bound on the number of input functions required by a threshold gate implementing a given function; (2) a lower bound on the error incurred when a Boolean function is approximated by a linear combination of a set of functions; (3) a limit on the effectiveness of a well known lower-hound technique (based on computing correlations among Boolean functions) for the depth of threshold circuits implementing Boolean functions; (4) a construction showing that every Boolean function ƒ of n input variables is a threshold function of polynomially many input functions, none of which is significantly correlated with ƒ; (5) generalizations of some known results on threshold-circuit complexity, particularly those that are based on spectral analysis.
11 citations