Chaotic neural nets, computability and undecidability-toward a computational dynamics
Anno: 1995
Autori: Basti G., Perrone AL.
Affiliazione autori: Università Pontificia Gregoriana, Roma, Italy;
Università 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.
Giornale/Rivista: INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS
Volume: 10 (1) Da Pagina: 41 A: 69
Parole chiavi: periodic-orbitsDOI: 10.1002/int.4550100106Citazioni: 5dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2024-05-12Riferimenti tratti da Isi Web of Knowledge: (solo abbonati) Link per visualizzare la scheda su IsiWeb: Clicca quiLink per visualizzare la citazioni su IsiWeb: Clicca qui