Finite degree clones are undecidable
Logic in Computer Science
2019-09-09 v4 Rings and Algebras
Abstract
A clone of functions on a finite domain determines and is determined by its system of invariant relations (=predicates). When a clone is determined by a finite number of relations, we say that the clone is of finite degree. For each Minsky Machine we associate a finitely generated clone such that has finite degree if and only if halts, thus proving that deciding whether a given clone has finite degree is impossible.
Cite
@article{arxiv.1811.05056,
title = {Finite degree clones are undecidable},
author = {Matthew Moore},
journal= {arXiv preprint arXiv:1811.05056},
year = {2019}
}