On strong Mal'cev conditions for congruence meet-semidistributivity in a locally finite variety

TL;DR

This paper investigates specific digraphs and polymorphisms to establish strong Mal'cev conditions that characterize congruence meet-semidistributivity in locally finite varieties, combining theoretical and computational methods.

Contribution

It identifies optimal strong Mal'cev conditions for congruence meet-semidistributivity using computational and theoretical analysis of small digraphs.

Findings

Characterization of polymorphisms for 4- and 5-element digraphs

Development of computational tools in C and Paradox

Identification of conditions implying congruence meet-semidistributivity

Abstract

In this paper we examine four-element and five-element digraphs for existence of certain polymorphisms that imply congruence meet-semidistributivity in a locally finite variety. The results presented here occurred as an integral part of my research for optimal strong Mal'cev conditions describing the property mentioned. Most of the programming needed to obtain these results was done in C programming language but for some results we also used the model builder Paradox. The source codes and Paradox inputs will be presented here as well (appendices one and two of this paper contain the source codes; an example of Paradox input is given in section 6).