Calculus of Cost Functions
Logic
2017-03-07 v1
Abstract
Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive strength. We show that the class of additive cost functions describes the -trivial sets. We prove a cost function basis theorem, and give a general construction for building computably enumerable sets that are close to being Turing complete. This works dates from 2010 and was submitted in 2013 to the long-delayed volume "The Incomputable" arising from the 2012 Cambridge Turing year.
Cite
@article{arxiv.1703.01577,
title = {Calculus of Cost Functions},
author = {Andre Nies},
journal= {arXiv preprint arXiv:1703.01577},
year = {2017}
}