Chaotic neural nets, computability and undecidability-toward a computational dynamics

Year: 1995

Authors: Basti G., Perrone A.L.

Autors Affiliation: Universitą Pontificia Gregoriana, Roma, Italy;
Universitą di Roma, Dip. di Fisica, Italy;
INFN Sez. di Roma;
Istituto Nazionale di Ottica, Largo E. Fermi 6, Firenze, Italy

Abstract: In this article we intend to analyze a chaotic system from the standpoint of its computation capability. To pursue this aim, we refer to a complex chaotic dynamics that we characterize via its symbolic dynamics. We show that these dynamic systems are subjected to some typical undecidable problems. Particularly, we stress the impossibility of deciding on a unique invariant measure. This depends essentially on the supposition of the existence of a fixed universal grammar. The suggestion is thus of justifying a centextual redefinition of the grammar as a function of the same evolution of the system. We propose on this basis a general theorem for avoiding undecidable problems in computability theory by introducing a new class of recursive functions on different axiomatizations of numbers. From it a series expansion on n algebraic fields can be defined. In such a way, we are able to obtain a very fast extraction procedure of unstable periodic orbits from a generic chaotic dynamics. The computational efficiency of this algorithm allows us to characterize a chaotic system by the complete statistics of its unstable cycles. Some examples of these two techniques are discussed. Finally, we introduce the possibility of an application of this same class of recursive functions to the calculus of the absolute minimum of energy in neural nets, as far as it is equivalent to a well-formed formula of a first-order predicate calculus. (C) 1995 John Wiley and Sons, Inc.

Journal/Review: INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS

Volume: 10 (1)      Pages from: 41  to: 69

KeyWords: periodic-orbits
DOI: 10.1002/int.4550100106

Citations: 5
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-17
References taken from IsiWeb of Knowledge: (subscribers only)
Connecting to view paper tab on IsiWeb: Click here
Connecting to view citations from IsiWeb: Click here