We introduce a method of characterizing the complexity of the minima of a given function, of N variables, by means of the entropy, S(N), of a measure selected as follows: One chooses an algorithm which computes the minima, and assigns to a single minimum a probability equal to the (relative) measure of its basin of attraction. The behavior of S(N), for large N, gives a well defined entropy density sigma for the minima, with respect to the chosen minima-generating law. sigma characterizes the complexity of the minima in a rather natural way in the framework of information theory, i.e., the number of bits one uses to transmit one (typical) minimum configuration is similar or equal to N sigma/ln2.

Complexity of the Minimum Energy Configurations

MARINI BETTOLO MARCONI, Umberto;
1995

Abstract

We introduce a method of characterizing the complexity of the minima of a given function, of N variables, by means of the entropy, S(N), of a measure selected as follows: One chooses an algorithm which computes the minima, and assigns to a single minimum a probability equal to the (relative) measure of its basin of attraction. The behavior of S(N), for large N, gives a well defined entropy density sigma for the minima, with respect to the chosen minima-generating law. sigma characterizes the complexity of the minima in a rather natural way in the framework of information theory, i.e., the number of bits one uses to transmit one (typical) minimum configuration is similar or equal to N sigma/ln2.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11581/241970
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