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 result is a significant step towards classification of homogeneous 3-graphs, going beyond known classification results for homogeneous structures.

我们研究数据丰富的模型，例如具有数据的Petri网，其中转换的可执行性取决于所涉及的数据值之间的关系。在这种模型中，各种决策问题的可判定性状态可能取决于数据域的结构。根据WQO二分法猜想，如果一个数据域是同质的，那么它要么表现出良好的拟序性（在这种情况下，可判定性遵循标准参数），或者基本上所有判定问题对于该数据域上的Petri网都是不可判定的。

我们确认对数据域的猜想是3张图（带有2色边的图）。在技​​术水平上，此结果是朝均质3图分类迈出的重要一步，超越了均质结构的已知分类结果。