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

18B20 Categories of machines, automata
93B99 Controllability, observability, and system structure
68Q45 Formal languages and automata
Full Text: DOI
[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. · 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
[5] Arbib, M.A.; Manes, E.G., Foundations of system theory: decomposable systems, Automatica, 10, 285-302, (1974) · Zbl 0294.93002
[6] Arbib, M.A.; Zeiger, H.P., On the relevance of abstract algebra to control theory, Automatica, 5, 589-606, (1969) · Zbl 0199.49303
[7] Bainbridge, E.S., A unified minimal realization theory, with duality for machines in a hyperdoctrine, (), (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
[10] Goguen, J.A., Minimal realization of machines in closed categories, J. comp. syst. sci., 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. · 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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