Inherently Ambiguous Languages
Inherent ambiguity was proven with Parikh's theorem in 1961 by Rohit Parikh in an MIT research report.
While some context-free languages (the set of strings that can be generated by a grammar) have both ambiguous and unambiguous grammars, there exist context-free languages for which no unambiguous context-free grammar can exist. An example of an inherently ambiguous language is the union of with . This set is context-free, since the union of two context-free languages is always context-free. But Hopcroft & Ullman (1979) give a proof that there is no way to unambiguously parse strings in the (non-context-free) subset which is the intersection of these two languages.
Read more about this topic: Ambiguous Grammar
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