Abstract
Weighted context-free grammar (WCFG) is a quantitative extension of context-free grammar (CFG). It is known that unambiguous weighted automata (WA), finitely-ambiguous WA, polynomially-ambiguous WA and general WA over the tropical semiring have different expressive powers. We prove that there exists a similar ambiguity hierarchy of WCFG over the tropical semiring, using an extended Ogden's lemma. In addition, we prove that each of the classes of finitely-ambiguous, polynomially-ambiguous, and exponentially-ambiguous WCFG can be subdivided into a finer strict hierarchy. We further show that the hierarchy we proved is different from the known ambiguity hierarchy of unweighted CFG.
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