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Deciding the Existence of Minority Terms

Published online by Cambridge University Press:  24 October 2019

Alexandr Kazda
Affiliation:
Charles University, Prague, Czech Republic Email: alex.kazda@gmail.com
Jakub Opršal
Affiliation:
University of Durham, Durham, UK Email: jakub.oprsal@durham.ac.uk
Matt Valeriote
Affiliation:
McMaster University, Hamilton, Ontario, Canada Email: matt@math.mcmaster.ca
Dmitriy Zhuk
Affiliation:
Charles University, Prague, Czech Republic Lomonosov Moscow State University, Moscow, Russia Email: zhuk@intsys.msu.ru

Abstract

This paper investigates the computational complexity of deciding if a given finite idempotent algebra has a ternary term operation $m$ that satisfies the minority equations $m(y,x,x)\approx m(x,y,x)\approx m(x,x,y)\approx y$. 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.

Type
Article
Copyright
© Canadian Mathematical Society 2019

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Footnotes

Author A. K. was supported by Charles University grants PRIMUS/SCI/12 and UNCE/SCI/022; J. O. was supported by the European Research Council (Grant Agreement no. 681988, CSP-Infinity) and the UK EPSRC (Grant EP/R034516/1); M. V. was supported by the Natural Sciences and Engineering Council of Canada; D. Z. was supported by the Russian Foundation for Basic Research (grant 19-01-00200).

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