Caterpillar dualities and regular languages

TL;DR

This paper explores the relationship between caterpillar dualities and regular languages, providing a characterization of obstruction sets and a construction of duals for regular caterpillar families, linking them to certain logic-based problems.

Contribution

It introduces a novel characterization of obstruction sets in caterpillar dualities using regular languages and constructs duals for regular caterpillar families, connecting them to monadic linear Datalog programs.

Findings

Obstruction sets in caterpillar dualities can be characterized by regular languages.

Duals of regular caterpillar families can be constructed explicitly.

Duals correspond to constraint satisfaction problems definable by monadic linear Datalog.

Abstract

We characterize obstruction sets in caterpillar dualities in terms of regular languages, and give a construction of the dual of a regular family of caterpillars. We show that these duals correspond to the constraint satisfaction problems definable by a monadic linear Datalog program with at most one EDB per rule.