The degree diagram of undecidable problems of formal grammars

Authors:
Dennis F. Cudia
Affiliations:
University of Wisconsin Center System, Baraboo, Wisconsin
Venue:
ACM SIGACT News
Year:
1969

Citing 3
Cited 0

General Problems of Formal Grammars

Journal of the ACM (JACM)
Formal languages and their relation to automata

Formal languages and their relation to automata
Structure of undecidable problems in automata theory

SWAT '68 Proceedings of the 9th Annual Symposium on Switching and Automata Theory (swat 1968)

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Abstract

Let O be the degree of all solvable problems, let O' be the degree of unsolvability of the halting problem for Turing machines, let O'' be the degree of unsolvability of the problem of whether an arbitrary Turing machine eventually halts for only finitely many finite initial configurations, and let O''' be the degree of unsolvability of the problem of whether an arbitrary Turing machine never halts for only finitely many finite initial configurations. Let ≤ denote the partial ordering of Turing reducibility. Then using results and methods of 1. and 2., the following degree diagram refinement of a table of solvable and unsolvable problems, which appears in 3., p. 230, may be obtained.