• Publications
  • Influence
On the (semi)lattices induced by continuous reducibilities
  • A. Pauly
  • Mathematics, Computer Science
  • Math. Log. Q.
  • 12 March 2009
TLDR
Continuous reducibilities are a proven tool in Computable Analysis, and have applications in other fields such as Constructive Mathematics or Reverse Mathematics. Expand
  • 65
  • 6
  • PDF
On the topological aspects of the theory of represented spaces
  • A. Pauly
  • Mathematics, Computer Science
  • Comput.
  • 17 April 2012
TLDR
Represented spaces form the general setting for the study of computability derived from Turing machines. Expand
  • 80
  • 5
  • PDF
A topological view on algebraic computation models
TLDR
We investigate the topological aspects of some algebraic computation models, in particular the BSS-model. Expand
  • 21
  • 4
  • PDF
Closed choice and a Uniform Low Basis Theorem
TLDR
We show that with closed choice one can characterize several models of hypercomputation in a uniform framework using Weihrauch reducibility. Expand
  • 95
  • 3
  • PDF
On the algebraic structure of Weihrauch degrees
TLDR
We introduce two new operations (compositional products and implication) on Weihrauch degrees, and investigate the overall algebraic structure. Expand
  • 45
  • 3
  • PDF
Towards Synthetic Descriptive Set Theory: An instantiation with represented spaces
TLDR
Using ideas from synthetic topology, a new approach to descriptive set theory can be reinterpreted as the study of certain endofunctors, primarily in the category of represented spaces. Expand
  • 26
  • 3
  • PDF
Searching for an analogue of ATR in the Weihrauch lattice
TLDR
We search for an analogue of ATR0 in the Weihrauch lattice and conclude that the situation is complicated. Expand
  • 10
  • 3
  • PDF
How Incomputable is Finding Nash Equilibria?
  • A. Pauly
  • Computer Science
  • J. Univers. Comput. Sci.
  • 2010
TLDR
We investigate the Weihrauch-degree of several solution concepts from noncooperative game theory in a meta-mathematical framework for real number computation. Expand
  • 54
  • 2
  • PDF
Relative computability and uniform continuity of relations
TLDR
A type-2 computable real function is necessarily continuous; and this remains true for relative, i.e. oracle-based, computations. Expand
  • 34
  • 2
  • PDF
Weihrauch Complexity in Computable Analysis
TLDR
We provide a self-contained introduction into Weihrauch complexity and its applications to computable analysis. Expand
  • 38
  • 2
  • PDF
...
1
2
3
4
5
...