"A Survey of Results on the d-c.e. and n-c.e. Degrees" provides a comprehensive overview of the d-c.e. (dynamically c.e.) and n-c.e. (nondeterministically c.e.) degrees. The authors, M.M. Arslanov and I.S. Kalimullin, present a survey of various results and findings related to these degrees. The d-c.e. and n-c.e. degrees are important concepts in computability theory and complexity theory, and the article explores their properties, relationships, and applications. By summarizing the existing research and highlighting key results, this article serves as a valuable resource for researchers and students interested in the field of theoretical computer science.
What is the definition and significance of the d-c.e. and n-c.e. degrees?
The authors provide definitions and explain the importance of these degrees in computability theory.
What are the basic properties and characteristics of d-c.e. and n-c.e. degrees?
The authors discuss fundamental properties such as closure under Turing reductions, enumeration properties, and relationships to other degrees.
What are the key results and findings related to d-c.e. and n-c.e. degrees?
The authors summarize important theorems, proofs, and discoveries in the field, highlighting the advancements made in understanding these degrees.
How are d-c.e. and n-c.e. degrees related to other concepts in computational complexity?
The authors explore connections between these degrees and other complexity classes, such as the polynomial hierarchy or the arithmetical hierarchy.
What are the open problems and future research directions in this area?
The authors discuss unresolved questions and suggest potential avenues for further investigation and research in the study of d-c.e. and n-c.e. degrees.