## Automata-theoretic aspects of formal power seriesDevoted to the theory of formal power series. Develops the theory for series in noncommuting variables. Emphasizes results applicable to automata & formal language theory. |

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### Contents

Introduction | 1 |

Rational series | 16 |

Applications of rational series | 76 |

Copyright | |

3 other sections not shown

### Common terms and phrases

4-algebraic A-rational algebraic series alphabet Assume automata automaton belongs characteristic series coefficients columns of H(r commutative semiring component Consider context-free grammar context-free languages Corollary decidable defined definition denote DOL sequence DOL system DTOL series Dyck language elements entries equals equation exercise Fatou extension finite formal language theory formal power series free monoid given grammar G Greibach normal form growth functions growth order Hadamard product Hankel matrices Hence implies induction integer integral domain Lemma letters lg(w mapping matrix N-rational n-tuple natural number obtained one-letter PDOL PDTOL polynomial problem proof of Theorem proper algebraic system prove pushdown automaton Q-stochastic quasiregular rational series regular language regulated rational transduction representation respectively right sides root of unity satisfied Section semi-algebraic sequence r(n Show solution stochastic languages subfield subring system G Theorem 2.3 variables word Z-rational sequence zero