Computation with Advice
Vasco Brattka,Arno Pauly +1 more
- Vol. 24, pp 41-55
TLDR
Computation with advice as discussed by the authors is a generalization of both computation with discrete advice and Type-2 Nondeterminism, and it has been shown that correct solutions are guessable with positive probability.Abstract:
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.read more
Citations
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Journal ArticleDOI
On uniform relationships between combinatorial problems
TL;DR: Weihrauch reducibility as mentioned in this paper has been studied in the context of combinatorial problems, and it has been used to compare and contrast with the traditional notion of implication in reverse mathematics.
Journal ArticleDOI
On the topological aspects of the theory of represented spaces
TL;DR: 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.
Journal ArticleDOI
Non-deterministic computation and the Jayne-Rogers Theorem
Arno Pauly,Matthew de Brecht +1 more
TL;DR: This work provides a simple proof of a computable analogue to the Jayne Rogers Theorem from descriptive set theory and demonstrates that developments in computational models can have applications in fields thought to be far removed from it.
Journal ArticleDOI
Real computation with least discrete advice: A complexity theory of nonuniform computability with applications to effective linear algebra
TL;DR: This work turns folklore into a both topological and combinatorial complexity theory of information, investigating for several practical problems how much advice is necessary and sufficient to render them computable.
Journal ArticleDOI
Searching for an analogue of atr0 in the weihrauch lattice
TL;DR: The situation is complicated: amongst the big five axiom systems from reverse mathematics, so far $\mathrm {ATR}_0$ has no identified counterpart in the Weihrauch degrees.
References
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Revising Type-2 Computation and Degrees of Discontinuity
TL;DR: The present work compares and unifies different relaxed notions of computability to cover also discontinuous functions based on the concept of the jump of a representation: both a TTE-counterpart to the well known recursion-theoretic jump on Kleene's Arithmetical Hierarchy of hypercomputation and a formalization of revising computation in the sense of Shoenfield.
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Vitali's Theorem and WWKL
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