Timed Sets, Functional Complexity, and Computability
source link: https://www.sciencedirect.com/science/article/pii/S1571066112000394
Go to the source link to view the article. You can view the picture content, updated content and better typesetting reading experience. If the link is broken, please click the button below to view the snapshot at that time.
Abstract
The construction of various categories of “timed sets” is described in which the timing of maps is considered modulo a “complexity order”. The properties of these categories are developed: under appropriate conditions they form discrete, distributive restriction categories with an iteration. They provide a categorical basis for modeling functional complexity classes and allow the development of computability within these settings. Indeed, by considering “program objects” and the functions they compute, one can obtain models of computability – i.e. Turing categories – in which the total maps belong to specific complexity classes. Two examples of this are introduced in some detail which respectively have their total maps corresponding to PTIME and LOGSPACE.
Recommend
About Joyk
Aggregate valuable and interesting links.
Joyk means Joy of geeK