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;
1995-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
