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Essentials of Petri nets

Wolfgang Reisig, Peter Fettke

TL;DR

This paper surveys Petri nets from their historical roots to contemporary compositional approaches, arguing for a theory of discrete dynamic, asynchronous systems grounded in logic and local causality. It traces developments from the late 1950s through the early 1980s, highlighting shifts from local steps to global markings, the emergence of data-bearing nets (colored nets, predicate transition nets), and the elm operator for predicate-based token interpretation. The core contribution centers on the composition problem, introducing Heraklit's two-faced interfaces and associative composition, and illustrating modular design with producer/consumer, claim settlement, coffee house, and light/fan examples. The work emphasizes modular, scalable reasoning about concurrency and offers a framework for building complex systems from reusable Petri-net modules with well-defined interfaces.

Abstract

This contribution highlights some concepts and aspects of Petri nets that are frequently neglected, but that the authors consider important or interesting, or that Carl Adam Petri emphasized.

Essentials of Petri nets

TL;DR

This paper surveys Petri nets from their historical roots to contemporary compositional approaches, arguing for a theory of discrete dynamic, asynchronous systems grounded in logic and local causality. It traces developments from the late 1950s through the early 1980s, highlighting shifts from local steps to global markings, the emergence of data-bearing nets (colored nets, predicate transition nets), and the elm operator for predicate-based token interpretation. The core contribution centers on the composition problem, introducing Heraklit's two-faced interfaces and associative composition, and illustrating modular design with producer/consumer, claim settlement, coffee house, and light/fan examples. The work emphasizes modular, scalable reasoning about concurrency and offers a framework for building complex systems from reusable Petri-net modules with well-defined interfaces.

Abstract

This contribution highlights some concepts and aspects of Petri nets that are frequently neglected, but that the authors consider important or interesting, or that Carl Adam Petri emphasized.
Paper Structure (11 sections, 6 equations, 26 figures)

This paper contains 11 sections, 6 equations, 26 figures.

Table of Contents

  1. The late 1950s
  2. The early 1960s
  3. The late 1960s
  4. The early 1970s
  5. The late 1970s
  6. The early 1980s
  7. Actual contribution: the composition problem
  8. A producer/consumer system
  9. Claim settlement
  10. Coffee house
  11. The light/fan system

Figures (26)

  • Figure 1: Carl Adam Petri in the late 1950s
  • Figure 2: Four steps of a bakery
  • Figure 3: A distributed run composed of four steps
  • Figure 4: Markings: global steps $M_0\xrightarrow[]{\text{bake}}M_1\xrightarrow[]{\text{supply to aide}}M_2\xrightarrow[]{\text{move to shop}}M_3\xrightarrow[]{\text{sell}}M_4$
  • Figure 5: Four seasons, intuitive model (a) and technical model (b)
  • ...and 21 more figures