Year: 2013
Type: preprint
Abstract: Termination property of functions is an important issue in computability theory. In this paper, we show that repeated iterations of a function can induce an order amongst the elements of its domain set. Hasse diagram of the poset, thus obtained, is shown to look like a forest of trees, with a possible base set and a generator set (defined in the paper). Isomorphic forests may arise for different functions and equivalences classes are, thus, formed. Based on this analysis, a study of the class of deterministically terminating functions is presented, in which the existence of a Self-Ranking Program, which can prove its own termination, and a Universal Terminating Function, from which every other terminating function can be derived, is conjectured.
Source: arXiv (Cornell University)
Authors: Aggarwal, Abhinav, Kumar, Padam
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2274305017