Characterize invariants determining equality of stochastic languages

Determine whether an invariant of a labelled partial order, under the paper’s specified scheduling law, can decide equality of the induced stochastic languages.

Background

The stochastic-language chart maps distributions over labelled partial orders to distributions over their observable linear extensions. This map is generally non-injective: genuine concurrency can induce the same stochastic language as a suitable mixture of sequential interleavings. The paper therefore asks whether some invariant of the underlying order alone could nevertheless characterize when two stochastic languages coincide. The answer may depend on the scheduling law, because a tilted law can assign different probabilities to interleavings and thereby expose information that is absent under the uniform law.

References

Whether some invariant of the order alone decides equality of stochastic languages is open, as is whether any log-derived channel is injective outright.

— Resolution limits for process comparison from event data  (2609.20489 - Lee et al., 17 Sep 2026) in Section 7, Discussion and conclusions, final discussion paragraph

Below the boundary Theorem~\ref{thm:kerL-linrel} characterises every kernel in advance, and only metric status is left open.

— Resolution limits for process comparison from event data  (2609.20489 - Lee et al., 17 Sep 2026) in Section 5, A dictionary of named comparisons, paragraph beginning “Below the boundary”