Regular families of forests, antichains and duality pairs of relational structures

TL;DR

This paper characterizes certain infinite-finite duality pairs involving forests and antichains in relational structures, advancing understanding of their complexity and structure in the context of homomorphism dualities.

Contribution

It provides a complete characterization of infinite-finite dualities with trees or forests on one side, extending previous work on antichain dualities in directed graphs.

Findings

Characterization of infinite-finite antichain dualities involving forests.

Identification of duality pairs with trees or forests on the left.

Extension of previous results on caterpillar dualities.

Abstract

Homomorphism duality pairs play crucial role in the theory of relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both side are infinite seems to be very complex. It is also known that no finite-infinite duality pair is possible if we make the additional restriction that both classes are antichains. In this paper we characterize the infinite-finite antichain dualities and infinite-finite dualities with trees or forest on the left hand side. This work builds on our earlier papers that gave several examples of infinite-finite antichain duality pairs of directed graphs and a complete characterization for caterpillar dualities.