Ambiguity in context free languages
Seymour Ginsburg, Joseph S. Ullian · Journal of the ACM · 1966
Four principal results about ambiguity in languages (i.e., context free languages) are proved. It is first shown that the problem of determining whether an arbitrary language is inherently ambiguous is recursively unsolvable. Then a decision procedure is presented for determining whether an arbitrary bounded grammar is ambiguous. Next, a necessary and sufficient algebraic condition is given for a bounded language to be inherently ambiguous. Finally, it is shown that no language contained in w 1 * w 2 *, each w 1 a word, is inherently ambiguous.