Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Computability
Complexity theory of real functions
Complexity theory of real functions
Handbook of formal languages, vol. 3
Computability on subsets of Euclidean space I: closed and compact subsets
Theoretical Computer Science - Special issue on computability and complexity in analysis
Index sets in computable analysis
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Recursive Automata on Infinite Words
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
Progress measures and finite arguments for infinite computations
Progress measures and finite arguments for infinite computations
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In this paper, we compare the computability and complexity of a continuous real function F with the computability and complexity of the graph G of the function F. A similar analysis will be carried out for functions on subspaces of the real line such as the Cantor space, the Baire space and the unit interval. In particular, we define four basic types of effectively closed sets C depending on whether (i) the set of closed intervals which with nonempty intersection with C is recursively enumerable (r.e.), (ii) the set of closed intervals with empty intersection with C is r.e., (iii) the set of open intervals which with nonempty intersection with C is r.e., and (iv) the set of open intervals with empty intersection with C is r.e. We study the relationships between these four types of effectively closed sets in general and the relationships between these four types of effectively closed sets for closed sets which are graphs of continuous functions.