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

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### Contents

Preface | 3 |

Examples of finite random categories | 38 |

Processes in finite random categories | 46 |

Copyright | |

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### Common terms and phrases

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 given Hadamard Hadamard matrix identical morphisms infinite process 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 morphisms p(y|x)€Hom(X,Y natural number Ob(C 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 rational algorithm reciprocal morphism respect sequence Shannon's entropy standard morphism stationary stationary process stochastic matrix subset tion two-person game type game type well-equipped utilities verify weighted entropy whichever