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DECIDING SOME MALTSEV CONDITIONS IN FINITE IDEMPOTENT ALGEBRAS

Part of: Algebraic structures General logic Theory of computing

Published online by Cambridge University Press:  16 June 2020

ALEXANDR KAZDA Open the ORCID record for ALEXANDR KAZDA [Opens in a new window]  and
MATT VALERIOTE Open the ORCID record for MATT VALERIOTE [Opens in a new window]
ALEXANDR KAZDA
Affiliation:
DEPARTMENT OF ALGEBRA CHARLES UNIVERSITYPRAGUE, CZECH REPUBLICE-mail: [email protected]
MATT VALERIOTE
Affiliation:
DEPARTMENT OF MATHEMATICS & STATISTICS MCMASTER UNIVERSITY, HAMILTON ONTARIO, CANADAE-mail: [email protected]
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Abstract

In this paper we investigate the computational complexity of deciding if the variety generated by a given finite idempotent algebra satisfies a special type of Maltsev condition that can be specified using a certain kind of finite labelled path. This class of Maltsev conditions includes several well known conditions, such as congruence permutability and having a sequence of n Jónsson terms, for some given n. We show that for such “path defined” Maltsev conditions, the decision problem is polynomial-time solvable.

Keywords

Maltsev conditionuniversal algebracomputational complexity

MSC classification

Primary: 68Q25: Analysis of algorithms and problem complexity
Secondary: 03B05: Classical propositional logic 08A40: Operations, polynomials, primal algebras
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 2 , June 2020 , pp. 539 - 562
Copyright
© The Association for Symbolic Logic 2020

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