The degree hierarchy of undecidable problems of formal grammars

Authors:
Dennis F. Cudia
Affiliations:
The University of Wisconsin, University Center System, Baraboo, Wisconsin
Venue:
STOC '70 Proceedings of the second annual ACM symposium on Theory of computing
Year:
1970

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Abstract

After a brief discussion of historical matters in §1, twenty-seven predicates of formal grammers are introduced in §2. The next two sections discuss recursively enumerable predicates and nonrecursively enumerable predicates, respectively. These results show that the degree of unsolvability of a predicate is determined by its domain of definition. The paper concludes with a degree diagram and suggestions for further development. From a more comprehensive point of view these results complement the computational complexity classification of solvable problems and extend that classification to unsolvable problems based on their degree of unsolvability.