Difference sets and computability theory

Diierence Sets and Computability Theory Zoltt an F Uredi

For a set A of non-negative integers, let D(A) (the diierence set of A) be the set of non-negative diierences of elements of A. Clearly, if A is computable, then D(A) is computably enumerable. We show (as partial converses) that every simple set which contains 0 is the diierence set of some computable set and that every computably enumerable set is computably isomorphic to the diierence set of ...

Computability of Convex Sets

We investigate computability of convex sets restricted to ra tional inputs Several quite di erent algorithmic characterizations are presented like the existence of e ective approximations by polygons or e ective line intersection tests We also consider approximate compu tations of the n fold characteristic function for several natural classes of convex sets This yields many di erent concrete ex...

Computability of Julia Sets

In this paper we settle most of the open questions on algorithmic computability of Julia sets. In particular, we present an algorithm for constructing quadratics whose Julia sets are uncomputable. We also show that a filled Julia set of a polynomial is always computable.

Computability Theory

Computability Theory

formalisms of computability