🤖 AI Summary
This study addresses the limitations in verifying high-order Petri net structural invariants within symmetric nets, which are currently restricted to specific subclasses. To overcome this, we propose an extended formal definition of symmetric nets that satisfies closure under fundamental operators, thereby establishing a more general invariant verification framework. Methodologically, this work integrates symbolic reachability graphs, discrete-event simulation, and formal calculus, leveraging the SNexpression tool to precisely compute symbolic structural relationships. Consequently, the proposed approach enables the semi-automatic verification of structural invariants, including (semi)flows, as well as flow family generation. The theoretical feasibility and the validity of the core concepts are demonstrated through representative examples.
📝 Abstract
Structural analysis is a core method in Petri Net (PN) research, offering a perspective complementary to state-space techniques while avoiding many of their limitations. It is well studied for classical PNs but far less for High-Level Petri Nets (HLPN). Symmetric Nets (SN), a common HLPN formalism, use compact annotations to encode behavioral symmetries, enabling the construction of a symbolic reachability graph (and a lumped Markov chain in stochastic SN) and the execution of symbolic discrete-event simulations. During the past two decades, structural techniques tailored to SN have been developed, notably supported by the SNexpression tool. This tool implements a formal calculus designed for the computation of symbolic structural relations, including, but not limited to, conflict relations and causal dependencies. Here, we focus on using this calculus to verify semi-automatically symbolic structural invariants, a task currently feasible only for certain restricted SN subclasses. We focus specifically on (semi)flows and briefly discuss an approach through which a flow generative family can be generated, at least theoretically. We further briefly outline a framework for the formal verification of a broader class of invariant properties. An extended formulation of the SN formalism is employed, which demonstrably satisfies the closure property with respect to fundamental functional operators. The core concepts are elucidated by means of representative examples throughout the exposition.