Three Analog Neurons Are Turing Universal

Authors: Jiří Šíma
Publication year: 2018
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Theory and Practice of Natural Computing
Projects: Center of excellence - Institute for theoretical computer science (CE-ITI)
Bibliographic citation: ŠÍMA, Jiří. Three Analog Neurons Are Turing Universal. In: FAGAN, D., MARTÍN-VIDE, C., O'NEILL, M., VEGA-RODRÍGUEZ, M.A., eds. Theory and Practice of Natural Computing. Cham: Springer, 2018, S. 460-472. Lecture Notes in Computer Science, 11324. ISBN 978-3-030-04069-7. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-030-04070-3_36
DOI: 10.1007/978-3-030-04070-3_36
ID: 490784

Abstract

The languages accepted online by binary-state neural networks with rational weights have been shown to be context-sensitive when an extra analog neuron is added (1ANNs). In this paper, we provide an upper bound on the number of additional analog units to achieve Turing universality. We prove that any Turing machine can be simulated by a binary-state neural network extended with three analog neurons (3ANNs) having rational weights, with a linear-time overhead. Thus, the languages accepted offline by 3ANNs with rational weights are recursively enumerable, which refines the classification of neural networks within the Chomsky hierarchy.