## Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical UseThis book presents a coherent description of the theoretical and practical aspects of Coloured Petri Nets (CP-nets or CPN). It shows how CP-nets have been de veloped - from being a promising theoretical model to being a full-fledged lan guage for the design, specification, simulation, validation and implementation of large software systems (and other systems in which human beings and/or com puters communicate by means of some more or less formal rules). The book contains the formal definition of CP-nets and the mathematical theory behind their analysis methods. However, it has been the intention to write the book in such a way that it also becomes attractive to readers who are more interested in applications than the underlying mathematics. This means that a large part of the book is written in a style which is closer to an engineering textbook (or a users' manual) than it is to a typical textbook in theoretical computer science. The book consists of three separate volumes. The first volume defines the net model (i. e. , hierarchical CP-nets) and the basic concepts (e. g. , the different behavioural properties such as deadlocks, fair ness and home markings). It gives a detailed presentation of many small exam ples and a brief overview of some industrial applications. It introduces the for mal analysis methods. Finally, it contains a description of a set of CPN tools which support the practical use of CP-nets. |

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### Contents

Informal Introduction to Coloured Petri Nets | 1 |

11 Introduction to PlaceTransition Nets | 2 |

12 Introduction to Coloured Petri Nets | 8 |

Distributed Data Base | 21 |

14 Net Inscriptions in CPN ML | 26 |

15 Construction of CPN Models | 32 |

16 Drawing of CPN Diagrams | 41 |

17 Some Important Advantages of CPnets | 50 |

43 Home Properties | 131 |

44 Liveness Properties | 132 |

45 Fairness Properties | 135 |

Bibliographical Remarks | 138 |

Formal Analysis of Coloured Petri Nets | 141 |

51 Occurrence Graphs | 142 |

52 Place and Transition Invariants | 147 |

53 Reduction Rules | 150 |

Bibliographical Remarks | 52 |

Exercises | 55 |

Formal Definition of Coloured Petri Nets | 65 |

21 Multisets | 66 |

22 Structure of NonHierarchical CPnets | 69 |

23 Behaviour of NonHierarchical CPnets | 73 |

24 Equivalent PlaceTransition Nets | 78 |

Bibliographical Remarks | 85 |

Hierarchical Coloured Petri Nets | 89 |

31 Introduction to Hierarchical CPnets | 90 |

Telephones | 99 |

33 Structure of Hierarchical CPnets | 106 |

34 Behaviour of Hierarchical CPnets | 113 |

35 Equivalent NonHierarchical CPnets | 115 |

Bibliographical Remarks | 119 |

Dynamic and Static Properties of Coloured Petri Nets | 123 |

41 Static Properties | 124 |

42 Boundedness Properties | 127 |

54 Performance Analysis | 152 |

Exercises | 153 |

Computer Tools for Coloured Petri Nets | 155 |

61 Editing of CPnets | 156 |

62 Simulation of CPnets | 176 |

63 Computer Tools for Formal Analysis | 194 |

Bibliographical Remarks | 202 |

Industrial Applications of Coloured Petri Nets | 205 |

71 Communication Protocol | 206 |

72 Hardware Chip | 209 |

73 Radar Surveillance | 213 |

74 Electronic Funds Transfer | 217 |

75 General Observations About CPN Applications | 218 |

Bibliographical Remarks | 219 |

221 | |

231 | |

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### Common terms and phrases

allows the user Analogously arc expressions behaviour Bibliographical Remarks binding elements bound Chap code segments colour set Coloured Petri Nets command complex consider constructed contains corresponding CPN diagram CPN editor CPN ML CPN model CPN simulator CPN tools data base system declarations defined denote described dialogue box e-tokens empty enabled binding equivalence relation evaluates example Exercise finite formal analysis methods function fusion set graphical guard hierarchical CP-net high-level nets IDEF identical initial marking initialization expressions inscriptions integer Intuitively invariants means multi-set nodes non-hierarchical CP-net non-hierarchical equivalent objects occurrence graph occurrence sequences operations page instances place instance group places and transitions port assignment possible prime page programming languages properties PT-net place PT-net transitions q-processes reachable marking represent resource allocation system ring network SADT sender shown in Fig specified Standard ML step structure subnet subpage substitution transitions supernode text strings tion token colours transition instance variables