Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use
This three-volume work presents a coherent description of the theoretical and practical aspects of coloured Petri nets (CP-nets). The second volume contains a detailed presentation of the analysis methods for CP-nets. They allow the modeller to investigate dynamic properties of CP-nets.
The main ideas behind the analysis methods are described as well as the mathematics on which they are based and also how the methods are supported by computer tools. Some parts of the volume are theoretical while others are application oriented. The purpose of the volume is to teach the reader how to use the formal analysis methods, which does not require a deep understanding of the underlying mathematical theory.
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Full Occurrence Graphs
11 Introduction to Ographs
12 Formal Definition of Ographs
13 Directed Paths and Strongly Connected Components
14 Proof Rules for Ographs
Distributed Data Base
17 Computer Tools for Ographs
35 Computer Tools for OSgraphs
41 Introduction to Place Invariants
42 Formal Definition of Place Invariants
43 Automatic Calculation of Place Invariants
44 Interactive Calculation of Place Invariants
Occurrence Graphs with Equivalence Classes
21 Introduction to OEgraphs
22 Formal Definition of OEgraphs
23 Proof Rules for OEgraphs
Distributed Data Base
26 Labelled OEgraphs
27 Computer Tools for OEgraphs
Occurrence Graphs with Symmetries
31 Symmetry Specifications
32 Proof Rules for OSgraphs
33 Permutation Symmetries
34 Labelled OSgraphs
45 Transition Invariants
46 Uniform CPnets
51 Introduction to Timed CPnets
52 Timed Multisets
53 Formal Definition of Timed CPnets
54 Relationships Between Timed and Untimed CPnets
56 Analysis of Timed CPnets
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algorithm Analogously arc expressions arc labels BE(c bi-implications bijective binding elements boundedness properties bounds calculate column compatible equivalence specification consider construct contains corresponding CPN tools data base managers data base system defined determined directed cycle directed graph dynamic properties end of Sect equivalence class equivalence relation Exercise fairness properties finite occurrence sequence formal definition Hence Id Id identical incidence matrix initial marking integer labelled OS-graph linear liveness properties maps means multi-set number of nodes O-graph occurrence graph tool output arc packet permutation symmetry philosopher system place flows place instance place invariants place weights possible process control system proof rules properties in Def prove PT-net reachable marking reduced matrix resource allocation system ring network rules in Prop SCC-graph self-symmetries stamp straightforward strongly connected component symmetry specification system from Sect tokens transition flows transition invariant untimed CP-net verify weighted-set
Page 169 - International Conference on Application and Theory of Petri Nets, Paris, France, June 1990. Reprinted in High-Level Petri Nets. Theory and Application, K. Jensen and G. Rozenberg (editors), Springer Verlag, 1991.
Page 170 - G. Rozenberg (eds.): Petri Nets: Central Models and Their Properties, Advances in Petri Nets 1986 Part I, Lecture Notes in Computer Science, vol. 254, Springer- Verlag 1987, 248-299. [Jen91] K. Jensen: Coloured Petri nets: A high level language for system design and analysis.