English

Deciding the existence of minority terms

Logic 2019-10-09 v2 Computational Complexity Rings and Algebras

Abstract

This paper investigates the computational complexity of deciding if a given finite idempotent algebra has a ternary term operation mm that satisfies the minority equations m(y,x,x)m(x,y,x)m(x,x,y)ym(y,x,x) \approx m(x,y,x) \approx m(x,x,y) \approx y. We show that a common polynomial-time approach to testing for this type of condition will not work in this case and that this decision problem lies in the class NP.

Keywords

Cite

@article{arxiv.1901.00316,
  title  = {Deciding the existence of minority terms},
  author = {Alexandr Kazda and Jakub Opršal and Matt Valeriote and Dmitriy Zhuk},
  journal= {arXiv preprint arXiv:1901.00316},
  year   = {2019}
}