Three Analog Neurons Are Turing Universal

0490784 - ÚI 2019 RIV CH eng C - Conference Paper (international conference)
Šíma, Jiří
Three Analog Neurons Are Turing Universal.
Theory and Practice of Natural Computing. Cham: Springer, 2018 - (Fagan, D.; Martín-Vide, C.; O'Neill, M.; Vega-Rodríguez, M.), s. 460-472. Lecture Notes in Computer Science, 11324. ISBN 978-3-030-04069-7. ISSN 0302-9743.
[TPNC 2018. International Conference on the Theory and Practice of Natural Computing /7./. Dublin (IE), 12.12.2018-14.12.2018]
R&D Projects: GA ČR GBP202/12/G061
Institutional support: RVO:67985807
Keywords : analog neural network * Turing machine * Chomsky hierarchy
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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.
Permanent Link: http://hdl.handle.net/11104/0284924