Process-tree definability of series-parallel poset languages

Characterize which languages of finite series-parallel labelled posets are denotable by process trees using sequence, parallel, exclusive-choice, and loop operators.

Background

The paper proves that the sequence-and-parallel fragment of process trees corresponds exactly to finite series-parallel partial orders. Once exclusive choice and loops are added, a process tree denotes a language—a finite or countably infinite set—of such posets. The unresolved issue is to characterize precisely which series-parallel-poset languages arise from this full process-tree syntax, since process-tree languages form a strict subclass of all series-parallel-poset languages.

A solution would provide a semantic characterization of process-tree expressiveness and clarify the relationship between process-tree syntax and the broader theory of series-parallel languages.

References

Section~\ref{subsec:open-problems} collects four open problems. It asks which series-parallel-poset languages a process tree can define, whether process trees admit a canonical form covering the loop operator, in what precise sense the BPMN normal form is faithful to its OR-gateway original, and whether POWL fits as a further instance of the general framework.

— String Diagrams for Process Mining  (2609.20478 - Lee et al., 17 Sep 2026) in Section 4.5, subsection “Open problems,” item 1; discussed also in Section 4.4 and Appendix B