A Note on Ambiguity of Context-Free Languages and Presentations of Semilinear Sets

An investigation is made of certain quantitative and qualitative aspects of inherent ambiguity of context-free languages. Two main results are proved. The first asserts that for every integer k there are inherently k-ambiguous context-free subsets of abc*. This result is obtained as a corollary of a more general result concerning ambiguous presentations of semilinear sets. The second result asserts that inherent ambiguity can arise from the “nesting” property of context-free languages, as well as from the “pairwise matching” property. © 1970, ACM. All rights reserved.