Abstract
Call a (context-free) language unambiguous if it is not inherently ambiguous. In the absence of evidence to the contrary, the suspicion has arisen that the unambiguous languages might be precisely those languages with context-free complements. The two theorems presented in this paper lay the suspicion to rest by providing (1) an inherently ambiguous language with context-free complement and (2) an unambiguous language without context-free complement. This establishes the independence of inherent ambiguity from complementedness among the context-free languages.
- 1 GINSBURG, S., AND SPANIR, E. H. Semigroups, Presburger formulas, and languages. Pacific J. Math. 16 (June 1966), 285-296.Google Scholar
- 2 Giusnua S., AND ULLIAN, J. Ambiguity in context free languages. J. ACM 13 (Jan. 1966), 62-89. Google Scholar
- 3 Koing, D. Theorie der endlichen und unendlichen Graphen. Chelsea Pub. Co., New York, 1950.Google Scholar
- 4 PAmH, R.J. Language-generating devices. Quart. Prog. Rep. No. 60, Res. Lab. of Electronics, MIT, Jan. 1961, pp. 199-212; reprinted with minor editorial revisions as: On context-free languages, J. ACM I5 (Oct. 1966), 570-581 (this issue).nGoogle Scholar
Index Terms
- The Independence of Inherent Ambiguity From Complementedness Among Context-Free Languages
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