PetriNetztheorie

PetriNetztheorie, also known as Petri net theory, is a mathematical modeling language for describing and analyzing distributed systems. Developed by Carl Adam Petri in 1962, it provides a graphical and mathematical framework to represent concurrent processes, resource sharing, and communication between different parts of a system.

A Petri net consists of two main types of nodes: places, typically represented by circles, and transitions, represented by rectangles or bars. Places represent conditions or states, while transitions represent events or actions that can occur. The flow of control or data is represented by directed arcs connecting places to transitions and transitions to places. Additionally, tokens, small dots, are placed within places to indicate the current state of the system. A transition is enabled if all its input places contain a sufficient number of tokens. When an enabled transition fires, it consumes tokens from its input places and produces tokens in its output places, thus changing the state of the system.

Petri nets are used in various fields, including computer science for modeling concurrent software and hardware systems, manufacturing for workflow analysis, biology for modeling biochemical pathways, and communication protocols. Their graphical nature makes them intuitive to understand, while their mathematical foundation allows for formal analysis of properties such as reachability, boundedness, liveness, and fairness. These analytical capabilities enable the identification of potential deadlocks, race conditions, and other concurrency-related issues in system designs. Variants of basic Petri nets, such as colored Petri nets, timed Petri nets, and hierarchical Petri nets, have been developed to address more complex modeling requirements.