55 research outputs found
Computation with Advice
Computation with advice is suggested as generalization of both computation
with discrete advice and Type-2 Nondeterminism. Several embodiments of the
generic concept are discussed, and the close connection to Weihrauch
reducibility is pointed out. As a novel concept, computability with random
advice is studied; which corresponds to correct solutions being guessable with
positive probability. In the framework of computation with advice, it is
possible to define computational complexity for certain concepts of
hypercomputation. Finally, some examples are given which illuminate the
interplay of uniform and non-uniform techniques in order to investigate both
computability with advice and the Weihrauch lattice
The descriptive theory of represented spaces
This is a survey on the ongoing development of a descriptive theory of
represented spaces, which is intended as an extension of both classical and
effective descriptive set theory to deal with both sets and functions between
represented spaces. Most material is from work-in-progress, and thus there may
be a stronger focus on projects involving the author than an objective survey
would merit.Comment: survey of work-in-progres
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