WQO dichotomy for 3-graphs

TL;DR

This paper confirms the WQO Dichotomy Conjecture for data domains modeled as 3-graphs, showing a clear divide between decidability and undecidability in Petri nets with data over these structures.

Contribution

It proves the WQO Dichotomy Conjecture specifically for 3-graph data domains, advancing classification results for homogeneous structures.

Findings

Confirmed the conjecture for 3-graphs

Established a dichotomy between decidability and undecidability

Extended classification results for homogeneous structures

Abstract

We investigate data-enriched models, like Petri nets with data, where executability of a transition is conditioned by a relation between data values involved. Decidability status of various decision problems in such models may depend on the structure of data domain. According to the WQO Dichotomy Conjecture, if a data domain is homogeneous then it either exhibits a well quasi-order (in which case decidability follows by standard arguments), or essentially all the decision problems are undecidable for Petri nets over that data domain. We confirm the conjecture for data domains being 3-graphs (graphs with 2-colored edges). On the technical level, this results is a significant step beyond known classification results for homogeneous structures.