[Paper Review] Reconfigurable Decorated PT Nets with Inhibitor Arcs and Transition Priorities

Julia Padberg|arXiv (Cornell University)|Sep 24, 2014

Petri Nets in System Modeling7 references3 citations

TL;DR

This paper introduces reconfigurable decorated P/T nets enhanced with inhibitor arcs and transition priorities, enabling dynamic structural changes and controlled firing behavior. The model extends reconfigurable Petri nets with semantic constraints—ensuring transitions fire only when specific places are empty (inhibitor arcs) or according to a defined priority order—while preserving $ abla$-adhesiveness, thus supporting formal verification and safe system evolution in dynamic environments.

ABSTRACT

In this paper we deal with additional control structures for decorated PT Nets. The main contribution are inhibitor arcs and priorities. The first ensure that a marking can inhibit the firing of a transition. Inhibitor arcs force that the transition may only fire when the place is empty. an order of transitions restrict the firing, so that an transition may fire only if it has the highest priority of all enabled transitions. This concept is shown to be compatible with reconfigurable Petri nets.

Motivation & Objective

• To extend reconfigurable decorated P/T nets with inhibitor arcs to model conditional firing based on place emptiness.
• To integrate transition priorities into the net model to enforce firing order among enabled transitions.
• To ensure compatibility with the $ abla$-adhesive category framework, enabling formal analysis of structural and behavioral evolution.
• To support dynamic system modeling in contexts like mobile networks and adaptive workflows where structural reconfiguration and controlled execution are essential.
• To provide a foundation for extending tools like ReConNet with richer control mechanisms for simulation and verification.

Proposed method

• Introduces inhibitor arcs that prevent a transition from firing unless the associated place is empty, formalized via a condition on the marking.
• Defines transition priorities using a partial order on transitions, where a transition can fire only if it has the highest priority among all enabled transitions.
• Extends decorated P/T nets with names, labels, and renewable labels, allowing dynamic label updates during firing.
• Uses the category of partially ordered sets ($ abla$-adhesive HLR-category) to model priorities and prove that the resulting category remains $ abla$-adhesive.
• Applies the algebraic approach to Petri nets, defining nets as tuples $(P, T, ext{pre}, ext{post}, M)$ with additional structure for labels and priorities.
• Proves that both the inhibitor arc and priority extensions preserve $ abla$-adhesiveness, ensuring compatibility with formal transformation rules and verification techniques.

Experimental results

Research questions

• RQ1 How can inhibitor arcs be formally integrated into reconfigurable decorated P/T nets without breaking structural modularity?
• RQ2 What is the impact of introducing transition priorities on the behavioral and structural consistency of reconfigurable nets?
• RQ3 Can the combination of inhibitor arcs and transition priorities be modeled within a $ abla$-adhesive category framework to support formal verification?
• RQ4 How do these extensions affect the simulation and reachability analysis of dynamic systems modeled with reconfigurable nets?
• RQ5 What is the formal relationship between the extended net model and existing reconfigurable Petri net formalisms?

Key findings

• The addition of inhibitor arcs is conservative with respect to net behavior and preserves $ abla$-adhesiveness in the category of decorated P/T nets.
• Transition priorities are modeled using a partial order on transitions, ensuring that only the highest-priority enabled transition may fire.
• The category of decorated P/T nets with transition priorities, denoted $ abla$-adhesive, is proven to be $ abla$-adhesive with respect to strict injective place mappings and strict order-embedding transition mappings.
• The model supports dynamic system evolution through rule application and firing, enabling safe, controlled reconfiguration in systems like mobile ad-hoc networks and adaptive workflows.
• The formal framework is implemented in the ReConNet tool, which supports graphical modeling, simulation, and extension with negative application conditions and reachability graphs.
• The integration of inhibitor arcs and priorities does not compromise the formal verification capabilities of reconfigurable nets, as both extensions preserve the $ abla$-adhesive structure.