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.
CITATION STYLE
Bhattiprolu, V., Gordon, S., & Viswanathan, M. (2017). Extending Parikh’s theorem to weighted and probabilistic context-free grammars. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10503 LNCS, pp. 3–19). Springer Verlag. https://doi.org/10.1007/978-3-319-66335-7_1
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