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One Analog Neuron Cannot Recognize Deterministic Context-Free Languages
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SYSNO ASEP 0505945 Druh ASEP C - Konferenční příspěvek (mezinárodní konf.) Zařazení RIV D - Článek ve sborníku Název One Analog Neuron Cannot Recognize Deterministic Context-Free Languages Tvůrce(i) Šíma, Jiří (UIVT-O) RID, SAI, ORCID
Plátek, Martin (UIVT-O)Zdroj.dok. Neural Information Processing. Proceedings, Part III. - Heidelberg : Springer, 2019 / Gedeon T. ; Wong K.-W. ; Lee M. - ISBN 978-3-030-36717-6 Rozsah stran s. 77-89 Poč.str. 13 s. Forma vydání Tištěná - P Akce ICONIP 2019. International Conference on Neural Information Processing of the Asia-Pacific Neural Network /26./ Datum konání 12.12.2019 - 15.12.2019 Místo konání Sydney Země AU - Austrálie Typ akce WRD Jazyk dok. eng - angličtina Země vyd. DE - Německo Klíč. slova Neural computing ; Analog neuron hierarchy ; Deterministic context-free language ; Restart automaton ; Chomsky hierarchy Vědní obor RIV IN - Informatika Obor OECD Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) CEP GA19-05704S GA ČR - Grantová agentura ČR Institucionální podpora UIVT-O - RVO:67985807 EID SCOPUS 85076967283 DOI 10.1007/978-3-030-36718-3_7 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2020 Elektronická adresa https://www.springer.com/gp/book/9783030367176
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