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Deciding the Existence of Minority Terms

Published online by Cambridge University Press:  24 October 2019

Alexandr Kazda
Charles University, Prague, Czech Republic Email:
Jakub Opršal
University of Durham, Durham, UK Email:
Matt Valeriote
McMaster University, Hamilton, Ontario, Canada Email:
Dmitriy Zhuk
Charles University, Prague, Czech Republic Lomonosov Moscow State University, Moscow, Russia Email:


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.

© Canadian Mathematical Society 2019

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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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