🤖 AI Summary
This study investigates “persistent permutability” in Petri nets—the property that a non-persistent firing sequence can be reordered into a persistent one—and explores under which structural conditions this property guarantees global persistency. Focusing on a class of Petri nets generalizing free-choice nets, the work establishes, for the first time, that persistent permutability implies global persistency in several such net classes. This result is achieved by analyzing the interplay between choice mechanisms and the phenomenon of “confusion.” Within this framework, the paper provides a rigorous proof of Ochmański’s conjecture for these classes. Combining Petri net theory, concurrency semantics, and structural classification techniques, the research offers new theoretical tools and delineates precise applicability boundaries for verifying persistency.
📝 Abstract
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.
