Petri net
Overview
 
A Petri net is one of several mathematical modeling language
Modeling language
A modeling language is any artificial language that can be used to express information or knowledge or systems in a structure that is defined by a consistent set of rules...

s for the description of distributed systems. A Petri net is a directed bipartite graph
Bipartite graph
In the mathematical field of graph theory, a bipartite graph is a graph whose vertices can be divided into two disjoint sets U and V such that every edge connects a vertex in U to one in V; that is, U and V are independent sets...

, in which the nodes represent transitions (i.e. events that may occur, signified by bars) and places (i.e. conditions, signified by circles). The directed arcs describe which places are pre- and/or postconditions for which transitions (signified by arrows). Some sources state that Petri nets were invented in August 1939 by Carl Adam Petri
Carl Adam Petri
Carl Adam Petri was a German mathematician and computer scientist. He was born in Leipzig.Petri nets were invented in August 1939 by Carl Adam Petri – at the age of 13 – for the purpose of describing chemicalprocesses...

 – at the age of 13 – for the purpose of describing chemical
processes.

Like industry standards such as UML
Unified Modeling Language
Unified Modeling Language is a standardized general-purpose modeling language in the field of object-oriented software engineering. The standard is managed, and was created, by the Object Management Group...

 activity diagram
Activity diagram
Activity diagrams are graphical representations of workflows of stepwise activities and actions with support for choice, iteration and concurrency. In the Unified Modeling Language, activity diagrams can be used to describe the business and operational step-by-step workflows of components in a system...

s, BPMN and EPC
Event-driven process chain
An Event-driven Process Chain is a type of flowchart used for business process modelling. EPC's can be used for configuring an enterprise resource planning implementation, and for business process improvement.- Overview :...

s, Petri nets offer a graphical notation
Diagram
A diagram is a two-dimensional geometric symbolic representation of information according to some visualization technique. Sometimes, the technique uses a three-dimensional visualization which is then projected onto the two-dimensional surface...

 for stepwise processes that include choice, iteration, and concurrent execution.
Unlike these standards, Petri nets have an exact mathematical definition of their execution semantics, with a well-developed mathematical theory for process analysis.

A Petri net consists of places, transitions, and arc
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

s.
 
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