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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.5 pp.1184-1194

- Publication Date
- 2001/05/01

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

- Category

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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 -