## Mathematical structure of finite random cybernetic systems: lectures held at the Department for Automation and Information, July, 1971 |

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according algorithm of recognition arbitrary element automata Bayes morphism category theory characteristic fk communication channel composed correct response cybernetic systems cylinder sets defined denoted derived morphisms deterministic morphism diagram elementary event entities equality ergodic error smaller exists FINITE RANDOM CATEGORIES FR-category game theory given Hadamard Hadamard matrix identical morphisms infinite process information theory informational entropy input signal large number learning process learning system Let us consider Let us suppose Markov chain Markov measure Markov morphism mathematical mean payoff minimum distance morphism corresponding morphism of order natural number objective probabilities objects X,Y obtain Obviously phism possible probability distribution probability of occurrence product morphism product set PROOF pure strategies qualitative random automaton random distribution random morphism p(y|x random strategy rj rational algorithm reciprocal morphism respect sequence Shannon's entropy standard morphism p(x stationary stationary process stochastic matrix subset tion two-person game type game utilities verify weighted entropy well-equipped whichever