Canonical normal forms for process trees

Determine a canonical normal form and minimization theorem for process trees, including the loop operator, by defining an appropriate congruence based on the equational theory of pomsets.

Background

The paper establishes a canonical decomposition for process trees restricted to sequence and parallel operators, corresponding to finite series-parallel posets. It does not establish a canonical representation for full process trees containing exclusive choice and loops.

The unresolved problem is to define a suitable semantic congruence and prove a minimization result, particularly for loop structure, so that equivalent process-tree descriptions can be reduced to a unique or otherwise canonical representative.

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 2; discussed also in Section 4.4

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 3; discussed also in Section 4.4 and Section 3.5