## Algebraic and Structural Automata TheoryAutomata Theory is part of computability theory which covers problems in computer systems, software, activity of nervous systems (neural networks), and processes of live organisms development. The result of over ten years of research, this book presents work in the following areas of Automata Theory: automata morphisms, time-varying automata, automata realizations and relationships between automata and semigroups. Aimed at those working in discrete mathematics and computer science, parts of the book are suitable for use in graduate courses in computer science, electronics, telecommunications, and control engineering. It is assumed that the reader is familiar with the basic concepts of algebra and graph theory. |

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### Contents

1 | |

7 | |

Chapter 2 Finite automata | 35 |

Chapter 3 Minimization of automata | 83 |

Chapter 4 Input subautomata | 119 |

Chapter 5 Automata homomorphisms | 155 |

Chapter 6 Realizations of automata State assignment | 197 |

Chapter 7 Realizations of automata Structures of nets | 229 |

Chapter 8 Timevarying automata | 269 |

Chapter 9 Transforms and extensions of automata | 301 |

Chapter 10 Periodic sums of automata | 319 |

Chapter 11 Linear automata | 347 |

371 | |

387 | |

### Common terms and phrases

algebra algorithm arbitrary assignment automata A0 automata theory automaton A=(S automorphisms autonomous factors bijections block called card(S characteristic semigroup components computation condition configuration Corollary cycle decomposition defined as follows definition denoted determine deterministic diagram elements equivalence relation Example exists finite automata fixed analog fixed automaton function f given automaton grammar graph Hom(A incomplete automaton input alphabet input subautomata isomorphic language accepted lattice Lemma Let A=(S Let us assume linear automaton linear bounded automaton Mikolajczak minimal minimal automaton natural number nondeterministic nonempty NP-complete output function partition pairs periodic automaton periodic sum permutation permutation automaton presented problem Proof properties psum,(A pushdown automaton Q.E.D. Theorem regular expression regular languages respect semigroup sequence shift register SP-partitions Step strong connectedness strongly connected structure subautomaton subset sum of automata symbol Table tape time-varying automaton transforms transition function Turing machine type automaton