Industrial Engineering Assignment
Presented by:
Chetan Rahate,
Section A, 22
PGDIE 42
Summary of research paper on :
Turing’s analysis of computation and artificial neural networks
Authors:
Wilson R. de Oliveiraa
Marc´ılio C. P. de Soutob and
Teresa B. Ludermirc
cCentro de Inform´atica, UFPE, Av.Professor Luis Freire, s/n, 50740-540, Recife, PE, Brazil
E-mail: tbl@cin.ufpe.br
Reference:
Journal of Intelligent & Fuzzy Systems 13 (2002/2003) 85–98 85
IOS Press
Summary:
A simplest way to simulate Turing Machines (TMs) by Artificial Neural Networks (ANNs) is proposed. The paper claims that the proposed simulation is in agreement with the correct interpretation of Turing’s analysis of computation; compatible with the current approaches to analyze cognition as an interactive agent-environment process; and physically realizable since it does not use connection weights with unbounded precision. A full description of an implementation of a universal TM into a recurrent sigmoid ANN focusing on the TM finite state control is given, leaving the tape, an infinite resource, as an external non-intrinsic feature. Also, motivated by the results on the limit of what can actually be computed by ANNs when noise is taken into account, author introduces the notion of Definite Turing Machine and investigate some of its properties.
Keywords:
Turing machine, recurrent sigmoid neural networks, mealy automata, definite automata
This paper is seminal to both the field of Artificial Neural Network (ANN) and to that of Automata Theory. Their logical model of the behavior of the nervous system turned out to be model of a Finite State Machine (FSM). Regarding universal computation – the relationship between ANNs and Turing Machines – an odd situation arise. While computer scientists (automata theoreticians) agree that a TMis a finite state automata with an external auxiliary memory realized as a read-write tape and free-moving head.
Definition included:
A Turing Machine T over a finite alphabet Σ is a quintuple T = (ΣT,QT , δT , sI,DT ), (the subscripts are used when necessary) where: (1) Q = {q1, . . . , q|Q|} is a finite set of states with a distinguished (initial) state, qI (usually q1); (2) δ : Q×Σ →W.R. de Oliveira et al. / Turing’s analysis of computation and artificial neural networks 87 Q× Σ× D is a function.
Conclusion:
By focusing on the implementation of the finite control of a ™ the auhors are thus led to the huge amount of work on finite state automata implementation on neural networks and learning, a subject not tackled in this work but which obviously is a next step.
Presented by:
Chetan Rahate,
Section A, 22
PGDIE 42
Summary of research paper on :
Turing’s analysis of computation and artificial neural networks
Authors:
Wilson R. de Oliveiraa
Marc´ılio C. P. de Soutob and
Teresa B. Ludermirc
cCentro de Inform´atica, UFPE, Av.Professor Luis Freire, s/n, 50740-540, Recife, PE, Brazil
E-mail: tbl@cin.ufpe.br
Reference:
Journal of Intelligent & Fuzzy Systems 13 (2002/2003) 85–98 85
IOS Press
Summary:
A simplest way to simulate Turing Machines (TMs) by Artificial Neural Networks (ANNs) is proposed. The paper claims that the proposed simulation is in agreement with the correct interpretation of Turing’s analysis of computation; compatible with the current approaches to analyze cognition as an interactive agent-environment process; and physically realizable since it does not use connection weights with unbounded precision. A full description of an implementation of a universal TM into a recurrent sigmoid ANN focusing on the TM finite state control is given, leaving the tape, an infinite resource, as an external non-intrinsic feature. Also, motivated by the results on the limit of what can actually be computed by ANNs when noise is taken into account, author introduces the notion of Definite Turing Machine and investigate some of its properties.
Keywords:
Turing machine, recurrent sigmoid neural networks, mealy automata, definite automata
This paper is seminal to both the field of Artificial Neural Network (ANN) and to that of Automata Theory. Their logical model of the behavior of the nervous system turned out to be model of a Finite State Machine (FSM). Regarding universal computation – the relationship between ANNs and Turing Machines – an odd situation arise. While computer scientists (automata theoreticians) agree that a TMis a finite state automata with an external auxiliary memory realized as a read-write tape and free-moving head.
Definition included:
A Turing Machine T over a finite alphabet Σ is a quintuple T = (ΣT,QT , δT , sI,DT ), (the subscripts are used when necessary) where: (1) Q = {q1, . . . , q|Q|} is a finite set of states with a distinguished (initial) state, qI (usually q1); (2) δ : Q×Σ →W.R. de Oliveira et al. / Turing’s analysis of computation and artificial neural networks 87 Q× Σ× D is a function.
Conclusion:
By focusing on the implementation of the finite control of a ™ the auhors are thus led to the huge amount of work on finite state automata implementation on neural networks and learning, a subject not tackled in this work but which obviously is a next step.
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