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Theorem · external strengthened case

FPRD-RDV-T03

Reachability is decidable for nicely orderable actions

Exact statement

Under the paper's computability assumptions, reachability in reversible Petri nets with data is decidable for every nicely orderable group action.

StatusProved in a 2025 preprint under stronger effective hypotheses
External reviewThe source is an arXiv preprint; no peer-reviewed publication or external review of the FPRD exposition is asserted.

Context

The later algorithm removes the earlier well-order restriction but retains effective orbit operations and a stronger labelled-WQO condition.

Hypotheses and scope

  • The action is effectively oligomorphic.
  • A compatible computable total order or effective reduct is available.
  • Labelled monomial divisibility is a WQO for every WQO label set.

Proof or evidence

The source computes an equivariant Gröbner basis and applies ideal membership to reversible data-Petri-net reachability.

The decidable strengthened case →

Verification notes

The additional hypotheses are stated explicitly, and no conclusion is transferred to a weaker hypothesis set.

Limitations

  • The exact weaker problem remains open in this record.
  • No elementary or polynomial complexity bound is claimed.

Open work

Track the publication status and test whether the binomial case needs less than the full labelled-WQO hypothesis.