Products in a Category with Only One Object
Logic in Computer Science
2021-01-27 v1
Abstract
We consider certain decision problems for the free model of the theory of Cartesian monoids. We introduce a model of computation based on the notion of a single stack one-way PDA due to Ginsburg, Greibach and Harrison. This model allows us to solve problems such as (1) Given a finite set B of elements and an element F, is F a product of members of B? (2) Is the submonoid generated by the finite set B infinite? for certain fragments of the free Cartesian monoid. These fragments include the submonoid of right invertible elements and so our results apply to the Thompson-Higman groups.
Keywords
Cite
@article{arxiv.2101.10494,
title = {Products in a Category with Only One Object},
author = {Richard Statman},
journal= {arXiv preprint arXiv:2101.10494},
year = {2021}
}
Comments
In Proceedings ACT 2020, arXiv:2101.07888