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Deciding the Existence of Minority Terms

Part of: General logic Algebraic structures Theory of computing

Published online by Cambridge University Press:  24 October 2019

Alexandr Kazda ,
Jakub Opršal ,
Matt Valeriote  and
Dmitriy Zhuk
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
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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.

Keywords

Maltsev conditionminority termcomputational complexity

MSC classification

Primary: 68Q25: Analysis of algorithms and problem complexity
Secondary: 03B05: Classical propositional logic 08A40: Operations, polynomials, primal algebras
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 3 , September 2020 , pp. 577 - 591
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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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