Automata-theoretic Aspects of Formal Power Series

A-algebraic a₁ algebraic series alphabet Arat<<X Assume automata automaton belong to Arat<<X characteristic series coefficients columns of H(r commutative semiring component Consider context-free grammar context-free languages Corollary decidable defined denote DOL sequence DOL system DTOL series Dyck language elements entries equals equation exercise Fatou extension finite formal power series free monoid G₁ given grammar G Greibach normal form growth functions growth order h₁ Hadamard product Hence implies induction integer K-stochastic L₁ Lemma letters M₁ mapping matrix N-rational n-tuple natural number obtained one-letter P₁ PDOL polynomial proof of Theorem proper algebraic system prove pushdown automaton quasiregular r₁ r₂ rational series regular language regulated rational transduction representation respectively right sides root of unity S₁ satisfied Section semiring Show solution stochastic languages subfield system G Theorem Theorem 2.3 V₁ variables w₁ weighted context-free grammars word X₁ Y₁ Z-rational sequence zero