One Analog Neuron Cannot Recognize Deterministic Context-Free Languages

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F19%3A00505945" target="_blank" >RIV/67985807:_____/19:00505945 - isvavai.cz</a>

Result on the web

<a href="https://www.springer.com/gp/book/9783030367176" target="_blank" >https://www.springer.com/gp/book/9783030367176</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-36718-3_7" target="_blank" >10.1007/978-3-030-36718-3_7</a>

Result language

angličtina

Original language name

One Analog Neuron Cannot Recognize Deterministic Context-Free Languages

Original language description

We analyze the computational power of discrete-time recurrent neural networks (NNs) with the saturated-linear activation function within the Chomsky hierarchy. This model restricted to integer weights coincides with binary-state NNs with the Heaviside activation function, which are equivalent to finite automata (Chomsky level 3), while rational weights make this model Turing complete even for three analog-state units (Chomsky level 0). For an intermediate model alphaANN of a binary-state NN that is extended with alpha>=0 extra analog-state neurons with rational weights, we have established the analog neuron hierarchy 0ANNs subset 1ANNs subset 2ANNs subseteq 3ANNs. The separation 1ANNs subsetneq 2ANNs has been witnessed by the deterministic context-free language (DCFL) L_#={0^n1^n|n>=1} which cannot be recognized by any 1ANN even with real weights, while any DCFL (Chomsky level 2) is accepted by a 2ANN with rational weights. In this paper, we generalize this result by showing that any non-regular DCFL cannot be recognized by 1ANNs with real weights, which means (DCFLs-REG) subset (2ANNs-1ANNs), implying 0ANNs = 1ANNs cap DCFLs. For this purpose, we show that L_# is the simplest non-regular DCFL by reducing L_# to any language in this class, which is by itself an interesting achievement in computability theory.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GA19-05704S" target="_blank" >GA19-05704S: FoNeCo: Analytical Foundations of Neurocomputing</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Neural Information Processing. Proceedings, Part III

ISBN

978-3-030-36717-6

ISSN

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e-ISSN

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Number of pages

13

Pages from-to

77-89

Publisher name

Springer

Place of publication

Heidelberg

Event location

Sydney

Event date

Dec 12, 2019

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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