# What does it mean if a Petri net is live?

## What does it mean if a Petri net is live?

Definition. A Petri Net is live for an initial marking m0 if, for every reachable marking. m and every transition t, there exists a marking m ∈ R[m〉 which enables. t. If (N, m0) is a live system, then we also say that m0 is a live marking of.

## What is reachability in Petri nets?

Behavioral analysis considers (i) the initial marking of the Petri net and (ii) its reachability graph. The reachability graph of a Petri net is a directed graph, G = (V, E), where each node, v ∈ V, represents a reachable marking and each edge, e ∈ E, represents a transition between two reachable markings.

Why do we need Petri nets?

Places have infinite capacity by default, and transitions have no capacity, and cannot store tokens at all. With the rule that arcs can only connect places to transitions and vice versa, we have all we need to begin using Petri Nets.

Is the Petri net alive?

A Petri net is live if all transitions are live.

### What is reachable graph?

In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex can reach a vertex (and is reachable from ) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with and ends with .

### What is the initial marking M0 of the net?

m0: P → IN is the initial marking representing the initial distribution of tokens. −→ m . The semantics given on the previous slide is also called interleaving semantics (one transition fires at a time).

What is a continuous Petri net?

A Continuous Petri net is a structure N= (P,T, Pre, Post) where: P is the set of places represented (see Fig. 1) by circles, | P | = m is number of all places; in our case m =38 (see Fig. 2 );

What is a Petri net in math?

A simple (black and white) Petri net is a digraph with nodes that are places (circles) or transitions (rectangles). Nodes of different kind are connected together by means of arcs. Arcs are of two kinds: Input arcs that connect one place to one transition.

## What is a marking in Petri net diagram?

The configuration of tokens distributed over an entire Petri net diagram is called a marking . In the top figure (see right), the place p1 is an input place of transition t; whereas, the place p2 is an output place to the same transition.

## Is the execution of a Petri net deterministic?

Unless an execution policy (e.g. a strict ordering of transitions, describing precedence) is defined, the execution of Petri nets is nondeterministic: when multiple transitions are enabled at the same time, they will fire in any order.