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Computability
About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.
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TL;DR: In this article, it was shown that there are no minimal pairs for generic computability, answering a question of Jockusch and Schupp, and thus, there is no generic computation that correctly computes most of the bits of a subset A of A and never incorrectly computes any bits of A.
Abstract: A generic computation of a subset A of ℕ consists of a computation that correctly computes most of the bits of A, and never incorrectly computes any bits of A, but which does not necessarily give an answer for every input. The motivation for this concept comes from group theory and complexity theory, but the purely recursion theoretic analysis proves to be interesting, and often counterintuitive. The primary result of this paper is that there are no minimal pairs for generic computability, answering a question of Jockusch and Schupp.
23 citations
TL;DR: This work investigates a configuration of three toposes, which is regarded as describing a notion of relative computability, and deriving a modal calculus as its internal logic.
23 citations
23 citations
TL;DR: The case when S is a 1-manifold with boundary, not necessarily compact, is examined and it is shown that a similar result holds in this case under assumption that S has finitely many components.
Abstract: A semi-computable set S in a computable metric space need not be computable. However, in some cases, if S has certain topological properties, we can conclude that S is computable. It is known that if a semi-computable set S is a compact manifold with boundary, then the computability of \deltaS implies the computability of S. In this paper we examine the case when S is a 1-manifold with boundary, not necessarily compact. We show that a similar result holds in this case under assumption that S has finitely many components.
23 citations
TL;DR: If the ergodic decomposition of a stationary measure is finite, is this decomposition effective?
23 citations