78 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
Total Representations
Almost all representations considered in computable analysis are partial. We
provide arguments in favor of total representations (by elements of the Baire
space). Total representations make the well known analogy between numberings
and representations closer, unify some terminology, simplify some technical
details, suggest interesting open questions and new invariants of topological
spaces relevant to computable analysis.Comment: 30 page
Ideal presentations and numberings of some classes of effective quasi-Polish spaces
The well known ideal presentations of countably based domains were recently
extended to (effective) quasi-Polish spaces. Continuing these investigations,
we explore some classes of effective quasi-Polish spaces. In particular, we
prove an effective version of the domain-characterization of quasi-Polish
spaces, describe effective extensions of quasi-Polish topologies, discover
natural numberings of classes of effective quasi-Polish spaces, estimate the
complexity of the (effective) homeomorphism relation and of some classes of
spaces w.r.t. these numberings, and investigate degree spectra of continuous
domains
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