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arXiv · 2602.02352

Well-Formed Free-Choice Petri Nets Revisited

Petr Jancar·Eike Best·Raymond Devillers·Matej Ostadal
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Abstract

The theory of free-choice Petri nets is an established field, initiated in the 1970s by F. Commoner and M. Hack. We revisit well-formed free-choice nets (those admitting markings that are both live and bounded) and provide a new characterisation 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 highly symmetric arguments.

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Petr Jancar, Eike Best, Raymond Devillers, Matej Ostadal. 2026-02-02. Well-Formed Free-Choice Petri Nets Revisited. https://arxiv.org/abs/2602.02352

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