2021-06-18T09:47:31Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:000684172020-10-27T05:02:56Z00934:00989:06006:06069
Theory of Minimizing Linear Separation AutomataTheory of Minimizing Linear Separation Automataengオリジナル論文http://id.nii.ac.jp/1001/00068417/Articlehttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=68417&item_no=1&attribute_id=1&file_no=1Copyright (c) 2010 by the Information Processing Society of JapanDepartment of Computer Science, Graduate School of Electro-Communications, The University of Electro-CommunicationsNTT-IT CorporationDepartment of Computer Science, Graduate School of Electro-Communications, The University of Electro-CommunicationsYuji, NumaiYoshiaki, UdagawaSatoshi, KobayashiIn this paper, we theoretically analyze a certain extension of a finite automaton, called a linear separation automaton (LSA). An LSA accepts a sequence of real vectors, and has a weight function and a threshold sequence at every state, which determine the transition from some state to another at each step. Transitions of LSAs are just corresponding to the behavior of perceptrons. We develop the theory of minimizing LSAs by using Myhill-Nerode theorem for LSAs. Its proof is performed as in the proof of the theorem for finite automata. Therefore we find that the extension to an LSA from the original finite automaton is theoretically natural.In this paper, we theoretically analyze a certain extension of a finite automaton, called a linear separation automaton (LSA). An LSA accepts a sequence of real vectors, and has a weight function and a threshold sequence at every state, which determine the transition from some state to another at each step. Transitions of LSAs are just corresponding to the behavior of perceptrons. We develop the theory of minimizing LSAs by using Myhill-Nerode theorem for LSAs. Its proof is performed as in the proof of the theorem for finite automata. Therefore we find that the extension to an LSA from the original finite automaton is theoretically natural.AA11464803情報処理学会論文誌数理モデル化と応用（TOM）3283912010-03-171882-77802010-03-12