Transition submatrices in regular homing experiments and identification of sequential machines of known class using direct-sum transition matrices

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Abstract

In connection with the measurement and control of synchronous sequential machines, Das et al. recently proposed an approach to the solution of the problems using the transition matrix representation of the machine and its higher-order forms. In the present paper, by extending the transition matrix approach of Das et al., an approach based on transition submatrix is developed to solve the regular homing problem in synchronous sequential machines. In addition, the problem of identifying a machine of a known class is also considered. Since the proposed transition submatrix approach can simplify the matrix computations, and can reduce the amount of storage required by significantly reducing both the dimension and the order of the matrix being used, it not only retains all the advantages of the approach by Das et al., but it lends itself to even easier computer implementations as well.

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    This research was supported in part by the National Science Council of the Republic of China, and by the Natural Sciences and Engineering Research Council of Canada under Grant A 4750.

    Sunil R. Das is a Professor of Electrical Engineering at the University of Ottawa, Ottawa, Ontario, Canada. He holds a B.Sc. (Hons) in Physics, an M.Sc. (Tech) and a Ph.D. in Radiophysics and Electronics from the University of Calcutta, Calcutta, West Bengal, India. He previously held academic positions with the Institute of Radiophysics and Electronics, University of Calcutta, and the Institute of Computer Engineering of the National Chiao Tung University in Hsinchu, Taiwan, Republic of China. Dr Das has published extensively in the areas of switching and automata theory, logic design, fault-tolerant computing, microprogramming, computer architecture, graph theory and combinatorics. He was elected one of the delegates of the Good People, Good Deeds of the Republic of China in 1981 for his contributions in the field of research, and education. He is currently the Managing Editor of the IEEE VLSI Technical Bulletin, a publication of the IEEE Computer Society Technical Committee on VLSI.

    §

    Zen Chen received a B.S. from the National Taiwan University, Taipei, Taiwan, Republic of China, an M.S. from the Duke University, Durham, North Carolina and a Ph.D. from the Purdue University, West Lafayette, Indiana, all in Electrical Engineering. Since 1974, Dr Chen has been teaching at the National Chiao Tung University, Hsinchu, Taiwan, Republic of China, where he is currently a Professor of Computer Engineering. His areas of interests include pattern recognition, digital image processing, pictorial database, artificial intelligence, and multiprocessor systems design.

    Yow Lung Dai earned his B.S. in Computer Science and Control Engineering and an M.S. in Computer Engineering from the National Chiao Tung University, Hsinchu, Taiwan, Republic of China. Mr Dai worked at Hewlett-Packard Taiwan as a Computer Staff Engineer and at the Taiwan Telecommunication Administration and Telecommunication Laboratories as a Systems Engineer. His fields of interest include computer architecture and organization, digital faults, reliable software, microprogramming, etc.

    Mrinal K. Das earned a B.Sc. (Hons) and an M.Sc. in Zoology from the University of Calcutta, Calcutta, West Bengal, India. He also holds an M.S. in Zoology from the University of Alberta, Edmonton, Alberta, Canada, where he is presently working towards his Ph.D. His research interests include ichthyology, zoogeography, freshwater ecology, and application of computer technology to these fields.

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