# Petri net

**Petri netsPetri net theoryconcurrent systemsP/T netsPetri-NetTimed-Arc Petri nets**

A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems.wikipedia

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### Carl Adam Petri

**Carl A. PetriPetri, Carl Adam**

Some sources state that Petri nets were invented in August 1939 by Carl Adam Petri—at the age of 13—for the purpose of describing chemical processes.

Petri created his major scientific contribution, the concept of the Petri net, in 1939 at the age of 13, for the purpose of describing chemical processes.

### Concurrency (computer science)

**concurrencyconcurrentconcurrently**

Since firing is nondeterministic, and multiple tokens may be present anywhere in the net (even in the same place), Petri nets are well suited for modeling the concurrent behavior of distributed systems.

A number of mathematical models have been developed for general concurrent computation including Petri nets, process calculi, the parallel random-access machine model, the actor model and the Reo Coordination Language.

### Modeling language

**modelling languageSoftware modelingsoftware modelling**

A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems.

### Activity diagram

**activitiesactivity modelActivity**

Like industry standards such as UML activity diagrams, Business Process Model and Notation and event-driven process chains, Petri nets offer a graphical notation for stepwise processes that include choice, iteration, and concurrent execution.

While in UML 1.x, activity diagrams were a specialized form of state diagrams, in UML 2.x, the activity diagrams were reformalized to be based on Petri net-like semantics, increasing the scope of situations that can be modeled using activity diagrams.

### Discrete event dynamic system

**discrete controldiscrete event systemsdiscrete-event systems**

It is a class of discrete event dynamic system.

### Reachability problem

**reachable**

The reachability problem for Petri nets is to decide, given a Petri net N and a marking M, whether M \in R(N).

Reachability is a fundamental problem that appears in several different contexts: finite- and infinite-state concurrent systems, computational models like cellular automata and Petri nets, program analysis, discrete and continuous systems, time critical systems, hybrid systems, rewriting systems, probabilistic and parametric systems, and open systems modelled as games.

### Diagram

**diagramsdiagrammatic formdiagrammatic**

Like industry standards such as UML activity diagrams, Business Process Model and Notation and event-driven process chains, Petri nets offer a graphical notation for stepwise processes that include choice, iteration, and concurrent execution.

### Nets within Nets

The term high-level Petri net is used for many Petri net formalisms that extend the basic P/T net formalism; this includes coloured Petri nets, hierarchical Petri nets such as Nets within Nets, and all other extensions sketched in this section.

Nets within Nets is a modelling method belonging to the family of Petri nets.

### CPN Tools

The term is also used specifically for the type of coloured nets supported by CPN Tools.

CPN Tools is a tool for editing, simulating, and analyzing high-level Petri nets.

### Bipartite graph

**bipartitebipartite graphsbipartiteness**

A Petri net is a directed bipartite graph, in which the nodes represent transitions (i.e. events that may occur, represented by bars) and places (i.e. conditions, represented by circles).

In computer science, a Petri net is a mathematical modeling tool used in analysis and simulations of concurrent systems.

### Event-driven process chain

**Event-driven Process ChainsEvent-driven process chains (EPC)**

Like industry standards such as UML activity diagrams, Business Process Model and Notation and event-driven process chains, Petri nets offer a graphical notation for stepwise processes that include choice, iteration, and concurrent execution.

### Dualistic Petri nets

Dualistic Petri nets (dPNs) are a process-class variant of Petri nets.

### Well-formed Petri net

Well-formed Petri nets are a Petri net class jointly elaborated between the University of Paris 6 (Université P. & M. Curie) and the University of Torino in the early 1990s.

### Stochastic Petri net

Stochastic Petri nets are a form of Petri net where the transitions fire after a probabilistic delay determined by a random variable.

### Prioritised Petri net

A Prioritised Petri net is a structure (PN, Π) where PN is a Petri net and Π is a priority function that maps transitions into non-negative natural numbers representing their priority level

### Vector addition system

**Vector addition system with statesvector addition system with states (VASS)**

Both VAS and VASS are equivalent in many ways to Petri nets introduced earlier by Carl Adam Petri.

### Marked graph

A marked graph is a Petri net in which every place has exactly one incoming arc, and exactly one outgoing arc. This means, that there can not be conflict, but there can be concurrency.

### Covering problems

**covering problemcoveringcovering LP**

Boundedness is decidable by looking at covering, by constructing the Karp–Miller Tree.

For Petri nets, for example, the covering problem is defined as the question if for a given marking, there exists a run of the net, such that some larger (or equal) marking can be reached.

### Concurrent computing

**concurrentconcurrent programmingconcurrency**

### EXPSPACE

**NEXPSPACEexponential spaceexponential space completeness**

In fact, this problem was shown to be EXPSPACE-hard years before it was shown to be decidable at all (Mayr, 1981).

The reachability problem for Petri Nets is EXPSPACE-hard.

### Workflow management system

**workflow managementWorkflow systemworkflow**

The underlying theoretical basis of workflow management is the mathematical concept of a Petri net.

### Process architecture

**architecturesprocess systems**

well-suited to being modeled by the bipartite Petri nets modeling system and in particular, process-class dualistic Petri nets where processes can be simulated in real time and space and studied hierarchically.

### Boolean differential calculus

**boolean derivativeboolean differencePotential variable (Boolean differential calculus)**

### Coloured Petri net

**Colored Petri netcoloured Petri nets**

Some of them are completely backwards-compatible (e.g. coloured Petri nets) with the original Petri net, some add properties that cannot be modelled in the original Petri net formalism (e.g. timed Petri nets).

Coloured Petri nets are a backward compatible extension of the mathematical concept of Petri nets.

### Process calculus

**process calculiprocess algebracalculus**

Other ways of modelling concurrent computation have been proposed, including process algebra, the actor model, and trace theory.

Models of concurrency such as the process calculi, Petri nets in 1962, and the actor model in 1973 emerged from this line of inquiry.