Persistent Permutability in Choice Petri Nets
For researchers in Petri net theory, this clarifies the relationship between persistent permutability and persistence, extending results beyond free-choice nets.
The paper identifies Petri net classes where persistent permutability (a weaker property than persistence) implies overall persistence, and proves Ochmanski's conjecture correct for these classes.
Persistence is a strong, global, behavioural property of a Petri net, meaning that no activity can disable a different activity. Persistent permutability is a weaker property, pertaining to individual interleavings of a Petri net and stating that a non-persistent sequence can be permuted into a persistent one. We identify Petri net classes for which persistent permutability already suffices to imply overall persistence. These classes generalise free-choice nets and are related to Petri's concept of ``confusion'', while they are distinguished from each other by diverse restrictions on the choice structure of a net. We prove Ochmanski's conjecture to be correct for these classes.