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Universality and Almost Decidability by Calude, Cristian S.; Desfontaines, Damien is a scholarly article available to read on EtoBox.

What is Universality and Almost Decidability about?

We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a decidable and generic (i.e. a set of natural density one) set whose intersection with S is decidable. Every decidable set is almost decidable, but the converse implication is false. We prove the existence of infinitely many universal functions whose halting sets are generic (negligible, i.e. have density zero) and (not) almost decidable. One result - namely, the existence of infinitely many universal functions whose halting sets are generic (negligible) and not almost decidable - solves an open problem in [9]. We conclude with some open problems.

Author

Calude, Cristian S.; Desfontaines, Damien

Published

2015

Language

EN