Coinductive properties of Lipschitz functions on streams
Dynamical Systems
2008-09-25 v1
Abstract
A simple hierarchical structure is imposed on the set of Lipschitz functions on streams (i.e. sequences over a fixed alphabet set) under the standard metric. We prove that sets of non-expanding and contractive functions are closed under a certain coiterative construction. The closure property is used to construct new final stream coalgebras over finite alphabets. For an example, we show that the 2-adic extension of the Collatz function and certain variants yield final bitstream coalgebras.
Keywords
Cite
@article{arxiv.0809.4187,
title = {Coinductive properties of Lipschitz functions on streams},
author = {Jiho Kim},
journal= {arXiv preprint arXiv:0809.4187},
year = {2008}
}