Petri网入门：建模技术、分析方法与实践案例

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"Understanding Petri Nets - Modeling Techniques, Analysis Methods, Case Studies" 是一本由Wolfgang Reisig编写的书籍，它详细介绍了Petri网的建模技术、分析方法和实际案例。这本书旨在为计算机科学和相关领域的学生、研究人员以及实践者提供一个清晰、全面的Petri网入门指南。 Petri网是一种图形化的建模工具，广泛应用于软件设计、控制工程等领域，具有直观且表达力强的特性。书中的第一部分主要讲解如何使用Petri网进行建模，通过实例逐步介绍基本概念，从一个通用且直观的模型入手，使读者能够理解其工作原理和实际应用。第二部分涉及Petri网特有的分析方法，包括验证系统网关键属性的技术和证明其有效性的算法。这部分内容对于深入理解Petri网的理论基础和分析技巧至关重要。第三部分通过一系列的案例研究，展示在不同建模任务中如何运用新概念、属性和分析技术。这些案例提供了多种学习路径，如针对仅对基本Petri网感兴趣的读者，针对希望学习建模但不涉及分析的读者，以及对简单但具有挑战性的案例和案例研究感兴趣的读者。本书的设计独特，注重一致性、可理解性和正确性。正式的论证在主文中尽可能简化，大部分理论形式化内容移至附录，全书贯穿图形插图以辅助解释，每章末尾还包含练习题和进一步阅读的推荐。 Wolfgang Reisig是柏林洪堡大学的教授，他在书中成功地平衡了理论深度和易读性，使得这本关于Petri网的著作既适合初学者，也适用于专业人士。书中的内容涵盖了ACM分类中的D.2（软件工程）、F.1（计算机系统实现）和I.6（离散数学）等相关领域。 "Understanding Petri Nets"是一本深入浅出的教程，它不仅介绍了Petri网的基本原理，还提供了实用的分析工具和丰富的案例，帮助读者掌握这一强大的建模工具，并能够在实际问题中灵活运用。

xviii Introduction

3.24.16 7 8 1011121415 1718192021

3.1

2.2

3.5 6.4

5.1

5.2

9.5

9.6

16.2

16.4

Figure 1 The elementary strand

3.2 4.5 7.1 7.6 8.1 9.3 19.1 21 22

3.4 4.6

20.1

20.4

Figure 2 The modeling strand

Readers who are interested in technically simple, but chal-

lenging examples and case studies can choose the elementary

models of the modeling strand, shown in Fig. 3.

3.2 7.1 7.6 8.1 19.1 21

3.1

3.4

20.1

20.4

Figure 3 The elementary modeling strand

How Is the Content Presented?

Pertinent examples and intuitive descriptions often explain the

content sufﬁciently well. In places where formal arguments are

used, only basic standard notations are employed, for instance,

for sets, functions, graphs, vectors, matrices, systems of equa-

xxii Contents

3.2 An Abstract Model of the Cookie Vending Machine ................ 26

3.3 Mutual Exclusion ...................................... 27

3.4 The Crosstalk Algorithm ................................. 28

3.5 1-Bounded Elementary System Nets .......................... 32

Exercises ............................................... 32

Further Reading ........................................... 33

4 Sequential and Distributed Runs ............................... 35

4.1 Sequential Runs ....................................... 35

4.2 Tokens as Labeled Places ................................. 37

4.3 Actions ............................................ 37

4.4 Distributed Runs ...................................... 39

4.5 Example: A Bell Clock .................................. 42

4.6 The Kindergarten Game .................................. 43

4.7 Causal Order ......................................... 45

4.8 The Composition of Distributed Runs ......................... 46

Exercises ............................................... 47

Further Reading ........................................... 48

5 Scenarios ............................................... 51

5.1 Deﬁning Scenarios ..................................... 51

5.2 The Scenarios of the Crosstalk Algorithm ....................... 53

5.3 The Scenarios of the Cookie Vending Machine .................... 54

Exercises ............................................... 55

Further Reading ........................................... 55

6 Further Notations for Elementary System Nets ...................... 57

6.1 Place Capacities ....................................... 57

6.2 Arc Weights ......................................... 58

6.3 Real Extensions ....................................... 61

Exercises ............................................... 62

Further Reading ........................................... 62

7 The Synthesis Problem ...................................... 65

7.1 Example: The Light/Fan System ............................ 65

7.2 The General Question of the Synthesis Problem ................... 67

7.3 Regions of State Automata ................................ 68

7.4 The System Net of a State Automaton

......................... 69

7.5 The Solution to the Synthesis Problem ......................... 70

7.6 The Synthesis Problem of the Light/Fan State Automaton ............. 70

Exercises ............................................... 71

Further Reading ........................................... 72

Contents xxiii

8 Composition of Nets ........................................ 75

8.1 Nets with Interfaces .................................... 75

8.2 C ommunicating Nets ................................... 78

8.3 Unambiguous Decomposition into Open Nets .................... 78

Exercises ............................................... 80

Further Reading ........................................... 80

Part II Analysis Methods

9 State Properties .......................................... 83

9.1 Equations and Inequalities of the Cookie Vending Machine ............ 83

9.2 Valid Equations ....................................... 86

9.3 Example: Dining Philosophers ............................. 86

9.4 Valid Inequalities ...................................... 88

9.5 Equations and Ineq ualities of Elementary System Nets .............. 88

9.6 Modulo Equations ..................................... 90

9.7 Propositional State Properties .............................. 91

Exercises ............................................... 93

Further Reading ........................................... 94

10 Traps and Cotraps of Elementary System Nets ...................... 97

10.1 Traps of Elementary System Nets ............................ 97

10.2 Cotraps ............................................ 98

10.3 The Trap/Cotrap Property ................................ 99

Exercises ............................................... 100

Further Reading ........................................... 101

11 Place Invariants of Elementary System Nets ........................ 103

11.1 Vector Representation for Elementary System Nets ................. 103

11.2 The Matrix N

........................................ 104

11.3 Place Invariants ....................................... 104

11.4 Positive Place Invariants ................................. 107

Exercises ............................................... 108

Further Reading ........................................... 109

12 Combining Traps and Place Invariants of Elementary System Nets ......... 111

12.1 Calculating with Equations and Inequalities ..................... 111

12.2 State Properties of the Mutual Exclusion System .................. 113

12.3 State Properties of the Crosstalk Algorithm ...................... 113

12.4 Unstable Properties .................................... 114

Exercises ............................................... 116

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