In the filed of cognitive psychology, simple recurrent networks are used for modeling the natural language processing in the human brain. For example, Elman experimentally showed that the simple recurrent networks can predict the right-most word in sentential forms of a particular grammar which can generate compound sentences with high probability. Concerning these results, it is natural to ask whether the computational capability of the simple recurrent networks is sufficient to recognize natural languages. In this paper, we assume that the range of a function computed at each gate of a simple recurrent network is a finite set. This is a quite realistic assumption, because we cannot physically implement a gate whose range is an infinite set. Then, we define equivalence relations between simple recurrent networks and Mealy machines or Moore machines, which are finite automata with output. Then, under our assumption, we show (1) a construction of a Mealy machine which simulates a given simple recurrent network, and (2) a construction of a simple recurrent network which simulates a given Moore machine. From these two constructions, we can conclude that the computational capability of the simple recurrent networks is equal to that of finite automata with output under our assumption.
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Junnosuke MORIYA, Tetsuro NISHINO, "Relationships between the Computational Capabilities of Simple Recurrent Networks and Finite Automata" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 5, pp. 1184-1194, May 2001, doi: .
Abstract: In the filed of cognitive psychology, simple recurrent networks are used for modeling the natural language processing in the human brain. For example, Elman experimentally showed that the simple recurrent networks can predict the right-most word in sentential forms of a particular grammar which can generate compound sentences with high probability. Concerning these results, it is natural to ask whether the computational capability of the simple recurrent networks is sufficient to recognize natural languages. In this paper, we assume that the range of a function computed at each gate of a simple recurrent network is a finite set. This is a quite realistic assumption, because we cannot physically implement a gate whose range is an infinite set. Then, we define equivalence relations between simple recurrent networks and Mealy machines or Moore machines, which are finite automata with output. Then, under our assumption, we show (1) a construction of a Mealy machine which simulates a given simple recurrent network, and (2) a construction of a simple recurrent network which simulates a given Moore machine. From these two constructions, we can conclude that the computational capability of the simple recurrent networks is equal to that of finite automata with output under our assumption.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_5_1184/_p
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@ARTICLE{e84-a_5_1184,
author={Junnosuke MORIYA, Tetsuro NISHINO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Relationships between the Computational Capabilities of Simple Recurrent Networks and Finite Automata},
year={2001},
volume={E84-A},
number={5},
pages={1184-1194},
abstract={In the filed of cognitive psychology, simple recurrent networks are used for modeling the natural language processing in the human brain. For example, Elman experimentally showed that the simple recurrent networks can predict the right-most word in sentential forms of a particular grammar which can generate compound sentences with high probability. Concerning these results, it is natural to ask whether the computational capability of the simple recurrent networks is sufficient to recognize natural languages. In this paper, we assume that the range of a function computed at each gate of a simple recurrent network is a finite set. This is a quite realistic assumption, because we cannot physically implement a gate whose range is an infinite set. Then, we define equivalence relations between simple recurrent networks and Mealy machines or Moore machines, which are finite automata with output. Then, under our assumption, we show (1) a construction of a Mealy machine which simulates a given simple recurrent network, and (2) a construction of a simple recurrent network which simulates a given Moore machine. From these two constructions, we can conclude that the computational capability of the simple recurrent networks is equal to that of finite automata with output under our assumption.},
keywords={},
doi={},
ISSN={},
month={May},}
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TY - JOUR
TI - Relationships between the Computational Capabilities of Simple Recurrent Networks and Finite Automata
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1184
EP - 1194
AU - Junnosuke MORIYA
AU - Tetsuro NISHINO
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2001
AB - In the filed of cognitive psychology, simple recurrent networks are used for modeling the natural language processing in the human brain. For example, Elman experimentally showed that the simple recurrent networks can predict the right-most word in sentential forms of a particular grammar which can generate compound sentences with high probability. Concerning these results, it is natural to ask whether the computational capability of the simple recurrent networks is sufficient to recognize natural languages. In this paper, we assume that the range of a function computed at each gate of a simple recurrent network is a finite set. This is a quite realistic assumption, because we cannot physically implement a gate whose range is an infinite set. Then, we define equivalence relations between simple recurrent networks and Mealy machines or Moore machines, which are finite automata with output. Then, under our assumption, we show (1) a construction of a Mealy machine which simulates a given simple recurrent network, and (2) a construction of a simple recurrent network which simulates a given Moore machine. From these two constructions, we can conclude that the computational capability of the simple recurrent networks is equal to that of finite automata with output under our assumption.
ER -