Semirings, Automata, Languages |
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a₁ a₂ Aalg AFP's algebraic system alphabet Arat Arat-T Assume automata theory automaton char claim coefficients commutative Consider context-free grammar context-free languages convergent sequences Corollary corresponding cycle-free defined definition denote discrete convergence equality follows family of power finite formal power series Furthermore Greibach normal form Hence i₁ idempotent iff there exists implies induction infer isomorphic isomorphic copy language theory Lemma M₁ M₂ mapping monoid morphism non-null entries normal form notation Observe obtain P₁ partially ordered polynomial principal cone proof of Theorem pushdown automata pushdown tape pushdown transition matrix Q₁ quasiregular r₁ r₂ regulated rational representation regulated rational transduction regulated representation reset type resp restart type right side Section semi-AFP semiring Show strong solution T₁ T₂ Theorem transition matrix u₁ unique solution v₁ variables w₁ w₂ y₁ ΜΕΣ πε πι Σ Σ ΣΤ ΧΕΣ