English

Well-Formed Free-Choice Petri Nets Revisited

Formal Languages and Automata Theory 2026-02-03 v1

Abstract

The theory of free-choice Petri nets is an established field, initiated in the 1970s by Commoner and Hack at MIT. We revisit well-formed free-choice nets (those admitting markings that are both live and bounded) and provide a new characterization by introducing semi-T-components. This notion is dual to that of semi-S-components, which in turn correspond to the well-known minimal siphons. By highlighting the symmetry between these dual concepts, we derive the classical coverability theorems for T- and S-components, as well as the duality theorem -- stating that a free-choice net is well-formed if and only if its reverse-dual is also well-formed -- using arguments that are as symmetric as possible.

Keywords

Cite

@article{arxiv.2602.02352,
  title  = {Well-Formed Free-Choice Petri Nets Revisited},
  author = {Petr Jancar and Eike Best and Raymond Devillers and Matej Ostadal},
  journal= {arXiv preprint arXiv:2602.02352},
  year   = {2026}
}