Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Topology via logic
Handbook of logic in computer science (vol. 1)
Handbook of logic in computer science (vol. 3)
Domains and lambda-calculi
Computability on subsets of Euclidean space I: closed and compact subsets
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
The Versatile Continuous Order
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
A Logic for Probabilities in Semantics
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Mathematical Structures in Computer Science
| Hi-index | 0.00 |
An element of an effectively given domain is computable iff its basic Scott open neighbourhoods are recursively enumerable. We thus refer to computable elements as Scott computable and define an element to be Lawson computable if its basic Lawson open neighbourhoods are recursively enumerable. Since the Lawson topology is finer than the Scott topology, a stronger notion of computability is obtained. For example, in the powerset of the natural numbers with its standard effective presentation, an element is Scott computable iff it is a recursively enumerable set, and it is Lawson computable iff it is a recursive set. Among other examples, we consider the upper powerdomain of Euclidean space, for which we prove that Scott and Lawson computability coincide with two notions of computability for compact sets recently proposed by Brattka and Weihrauch in the framework of type-two recursion theory.