Many problems in the theory of control systems reduce to the objects considered in the present paper -general linear automata. The necessity of studying them is manifested most clearly in the problem of reducing finite probabilistic automata [12, 13, 15, 19] which are an important particular case of general linear automata. On the other hand, many properties which apply to finite deterministic automata can be generalized successfully for the case of general linear automata, their proof turning out to be sometimes simpler than well-known proofs of analogous theorems for finite automata.
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- 3.A. Hill, Introduction to the Theory of Finite Automata [Russian translation], Mir, Moscow (1966).Google Scholar
- 5.N. E. Kobrinskii and B. A. Trakhtenbrot, Introduction to the Theory of Finite Automata [in Russian], Fizmatgiz, Moscow (1961), Chap. II, V, and VII.Google Scholar
- 6.A. D. Korshunov, “On the degree of distinguishability of automata,” in: Discrete Analysis, No. 10, Nauka, Novosibirsk (1967), pp. 39–60.Google Scholar
- 7.M. S. Lifshits, “On linear physical systems connected with the external world by communication channels,” Izvestiya Akad. Nauk SSSR, 27:993–1030 (1963).Google Scholar
- 9.A. A. Muchnik, “Length of an experiment for determining the structure of a finite strongly connected automaton,” in: Systems Theory Research, Vol. 20, Consultants Bureau, New York (1971), p. 136.Google Scholar
- 11.M. L. Tsetlin, “On nonprimitive networks,” in: Problemy Kibernetiki, Vol. 11, Fizmatgiz, Moscow (1958), p. 31.Google Scholar
- 12.G. Bacon, “Minimal-state stochastic finite-state systems,” Trans. IEEE, CT-ll:307–308 (1964).Google Scholar
- 18.E.F. Moore, Gedanken-Experiments on Sequential Machines. Automata Studies, Princeton University Press (1956), pp. 129–153.Google Scholar