The subpower membership problem of 2-nilpotent algebras
Rings and Algebras
2023-09-29 v1 Computational Complexity
Abstract
The subpower membership problem SMP(A) of a finite algebraic structure A asks whether a given partial function from A^k to A can be interpolated by a term operation of A, or not. While this problem can be EXPTIME-complete in general, Willard asked whether it is always solvable in polynomial time if A is a Mal'tsev algebras. In particular, this includes many important structures studied in abstract algebra, such as groups, quasigroups, rings, Boolean algebras. In this paper we give an affirmative answer to Willard's question for a big class of 2-nilpotent Mal'tsev algebras. We furthermore develop tools that might be essential in answering the question for general nilpotent Mal'tsev algebras in the future.
Keywords
Cite
@article{arxiv.2309.16549,
title = {The subpower membership problem of 2-nilpotent algebras},
author = {Michael Kompatscher},
journal= {arXiv preprint arXiv:2309.16549},
year = {2023}
}
Comments
17 pages (including appendix)