🤖 AI Summary
This study addresses the challenges of structural analysis in high-level Petri nets and the limitation of symmetric net invariant verification to restricted subclasses. It proposes a semi-automated method for verifying symbolic structural invariants within extended symmetric nets. By applying symbolic structural calculus to a formal framework closed under key functional operators, this work constructs a generating family framework focused on flow relations. Verification is achieved using the SNexpression tool, symbolic reachability graphs, lumped Markov chains, and conflict causality calculus. The research establishes a theoretical verification framework applicable to broader invariant properties and validates its core concepts through representative examples, significantly extending the applicability of invariant analysis.
📝 Abstract
Structural analysis is central to Petri Net (PN) research, complementing state-space methods while avoiding their combinatorial issues. It is well studied for classical PNs but much less for High-Level Petri Nets (HLPN). Symmetric Nets (SN), a common HLPN formalism, use compact annotations to encode behavioral symmetries, allowing symbolic reachability graphs and associated lumped Markov chains for stochastic SN. In the past two decades, specific structural techniques for SN have emerged, notably the SNexpression tool, which implements a calculus for symbolic structural relations such as conflict and causality. We propose using this calculus to semi-automatically verify symbolic structural invariants, currently possible only for restricted SN subclasses, for an extended SN formalism (ESN) closed under key functional operators. We focus on flows and outline, at least in theory, how to construct a flow-generating family. We also sketch a framework for formally verifying a wider range of invariant properties. Representative examples illustrate the main concepts.