## Algebraic Structures in Automata and Databases TheoryThe book is devoted to the investigation of algebraic structure. The emphasis is on the algebraic nature of real automation, which appears as a natural three-sorted algebraic structure, that allows for a rich algebraic theory. Based on a general category position, fuzzy and stochastic automata are defined. The final chapter is devoted to a database automata model. Database is defined as an algebraic structure and this allows us to consider theoretical problems of databases. |

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### Contents

PRELIMINARIES | 1 |

PURE AUTOMATA | 11 |

CONSTRUCTIONS AND DECOMPOSITION OF PURE AUTOMATA | 73 |

LINEAR AUTOMATA | 105 |

VARIETIES OF AUTOMATA | 155 |

AUTOMATA MODEL OF DATABASE | 237 |

269 | |

277 | |

### Common terms and phrases

0-simple 9 and 9 a°y a°y Atm F,B automa automaton 9 automaton 9=(A,F,B automaton A,F,B automaton Atm A,D automorphism belongs biautomaton binary relation called Cartesian product cascade connection class of biautomata compatible tuples completely characteristic congruence construction corresponding coset databases decomposition defined definition Denote determining mapping divisor embedded End(A,B epimorphism equality equivalence exact automaton F-identities finite free automaton free semigroup fuzzy given group automata group F Halmos algebras Hence homomorphic image homomorphism in input implies indecomposable input signals isomorphic kernel Lemma linear automata linear space maton monomorphism Moore automaton morphism n-algebra non-trivial operations output signals phism product of biautomata Proof Proposition pure automata quasiidentity query quotient set representation A,D satisfies the conditions semiautomaton semigroup automaton semigroup F subautomaton subgroup subset Take terminal object Theorem tion triangular product triplet tuple unique variety of biautomata verify wreath product