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