Nonexistence of minimal pairs for generic computability
G Igusa�- The Journal of Symbolic Logic, 2013 - cambridge.org
G Igusa
The Journal of Symbolic Logic, 2013•cambridge.orgA 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.
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.
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.
Cambridge University Press