On the (semi)lattices induced by continuous reducibilities
- A. Pauly
- Mathematics, ChemistryMathematical Logic Quarterly
- 12 March 2009
The order-theoretic properties of several variants of the two most important definitions of continuous reducibilities are studied, and suprema are shown to commutate with several characteristic numbers.
Weihrauch Complexity in Computable Analysis
A self-contained introduction into Weihrauch complexity and its applications to computable analysis and a survey on some classification results and a discussion of the relation to other approaches are provided.
A topological view on algebraic computation models
On the topological aspects of the theory of represented spaces
- A. Pauly
- MathematicsDe Computis
- 17 April 2012
This work presents an abstract and very succinct introduction to the theory of represented spaces, drawing heavily on prior work by Escardo, Schroder, and others.
On the algebraic structure of Weihrauch degrees
A function space of multi-valued continuous functions that turns out to be particularly well-behaved for effectively traceable spaces that are closely related to admissibly represented spaces is introduced and studied.
Descriptive Set Theory in the Category of Represented Spaces
This work can reformulate DST in terms of endofunctors on the categories of represented spaces and computable or continuous functions and satisfies the demand for a uniform approach to both classic and effective DST.
Closed choice and a Uniform Low Basis Theorem
How Incomputable is Finding Nash Equilibria?
- A. Pauly
- EconomicsJournal of universal computer science (Online)
The Weihrauch-degree of several solution concepts from noncooperative game theory, including pure and correlated equilibria, as well as various concepts of iterated strategy elimination, are investigated.
Towards Synthetic Descriptive Set Theory: An instantiation with represented spaces
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested, which mainly focuses on developing the ideas in the category of represented spaces.
The degree structure of Weihrauch-reducibility
This work answers a question by proving that the Weihrauch-lattice is not a Brouwer algebra, and investigates the existence of infinite infima and suprema, as well as embeddings of the Medvedev-degrees into the Weil-degree.