An ambiguity hierarchy of weighted context-free grammars

• Published in: Theoretical computer science Vol. 974; p. 114112
• Main Authors: Inoue, Yusuke, Hashimoto, Kenji, Seki, Hiroyuki
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 29.09.2023
• Subjects: Ambiguity; Pumping lemma; Weighted context-free grammar; Weighted context-free grammar; Pumping lemma; Ambiguity
• ISSN: 0304-3975
• DOI: 10.1016/j.tcs.2023.114112

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. •We proved that four subclasses of WCFGs over the tropical semiring have different expressive powers.•We proved that each of the classes mentioned in item 1 can be subdivided into a finer strict hierarchy.•We showed a pumping lemma for CFG, an extension of Ogden’s lemma. The lemma is helpful for proving the hierarchies.•We showed that the hierarchies mentioned above are different from the known ambiguity hierarchies of unweighted CFG.