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Adjoint machines, state-behavior machines, and duality. (English) Zbl 0323.18002


MSC:

18B20 Categories of machines, automata
93B99 Controllability, observability, and system structure
68Q45 Formal languages and automata
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References:

[1] B.D.O. Anderson, M.A. Arbib and E.G. Manes, Foundations of system theory: finitary and infinitary conditions, Springer Lecture Noted in Economics and Mathematical Systems, to appear.; B.D.O. Anderson, M.A. Arbib and E.G. Manes, Foundations of system theory: finitary and infinitary conditions, Springer Lecture Noted in Economics and Mathematical Systems, to appear. · Zbl 0462.93003
[2] Arbib, M. A., Theories of Abstract Automata (1969), Prentice-Hall · Zbl 0193.32801
[3] Arbib, M. A.; Manes, E. G., Machines in a category: an expository introduction, SIAM Review, 16, 163-192 (1974) · Zbl 0288.18005
[4] Arbib, M. A.; Manes, E. G., Fuzzy Machines in a Category, Bull. Australian Math. Soc., 13, 169-210 (1975) · Zbl 0318.18008
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[7] Bainbridge, E. S., A Unified minimal realization theory, with duality for machines in a hyperdoctrine, (Technical Report (1972), Computer and Communication Sciences Department, University of Michigan), (For the full thesis see “A Unified Minimal Realization Theory with Duality”, from the same group, November 1972.)
[8] Barr, M., Coequalizers and free triples, Math. Z., 116, 307-322 (1970) · Zbl 0194.01701
[9] Ehrig, H.; Kiermeier, K.-D.; Kreowski, M.-J.; Kühnel, W., Universal Theory of Automata (1974), Teubner · Zbl 0289.94023
[10] Minimal realization of machines in closed categories, Bull. Amer. Math. Soc., 78, 777-783 (1972) · Zbl 0277.18003
[11] Kalman, R. E.; Falb, P. L.; Arbib, M. A., Topics in Mathematical System Theory (1969), McGraw-Hill · Zbl 0231.49001
[12] McCarty, G., Topology (1967), McGraw-Hill · Zbl 0171.43401
[13] E.G. Manes, Algebraic Theories, Graduate texts in Mathematics 26 (Springer-Verlag) to appear.; E.G. Manes, Algebraic Theories, Graduate texts in Mathematics 26 (Springer-Verlag) to appear. · Zbl 0489.18003
[14] Rabin, M. O.; Scott, D., Finite automata and their decision problems, IBM. J. Res. and Dev., 3, 114-125 (1959) · Zbl 0158.25404
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