Waiting Nets: State Classes and Taxonomy

TL;DR

This paper introduces waiting nets, an extension of time Petri nets that decouples control and timing, enabling more flexible modeling and decidability of key properties.

Contribution

It proposes waiting nets, allowing time measurement to start with incomplete presets, and provides methods to analyze their reachability and expressiveness.

Findings

Finite state class graph can be computed for bounded waiting nets.

Waiting nets are more expressive than traditional TPNs.

Decidability of reachability and coverability is established for bounded waiting nets.

Abstract

In time Petri nets (TPNs), time and control are tightly connected: time measurement for a transition starts only when all resources needed to fire it are available. Further, upper bounds on duration of enabledness can force transitions to fire (this is called urgency). For many systems, one wants to decouple control and time, i.e. start measuring time as soon as a part of the preset of a transition is filled, and fire it after some delay \underline{and} when all needed resources are available. This paper considers an extension of TPN called waiting nets that dissociates time measurement and control. Their semantics allows time measurement to start with incomplete presets, and can ignore urgency when upper bounds of intervals are reached but all resources needed to fire are not yet available. Firing of a transition is then allowed as soon as missing resources are available. It is known that extending bounded TPNs with stopwatches leads to undecidability. Our extension is weaker, and we show how to compute a finite state class graph for bounded waiting nets, yielding decidability of reachability and coverability. We then compare expressiveness of waiting nets with that of other models w.r.t. timed language equivalence, and show that they are strictly more expressive than TPNs.