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    Extending Parikh's Theorem to Weighted and Probabilistic Context-Free Grammars

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    We prove an analog of Parikh's theorem for weighted context-free grammars over commutative, idempotent semirings, and exhibit a stochastic context-free grammar with behavior that cannot be realized by any stochastic right-linear context-free grammar. Finally, we show that every unary stochastic context-free grammar with polynomially-bounded ambiguity has an equivalent stochastic right-linear context-free grammar.Ope
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