Unifying Petri Nets: Advances in Petri Nets (Lecture Notes in Computer Science, 2128)

✍ Scribed by Hartmut Ehrig (editor), Gabriel Juhas (editor), Julia Padberg (editor), Grzegorz Rozenberg (editor)

• Publisher: Springer
• Year: 2001
• Tongue: English
• Leaves: 495
• Category: Library

✦ Synopsis

Since their introduction nearly 40 years ago, research on Petri nets has diverged in many different directions. Various classes of Petri net, motivated either by theory or applications, with its own specific features and methods of analysis, have been proposed and studies in depth.
These successful developments have led to a very heterogeneous landscape of diverse models, and this, in turn, has stimulated research on concepts and approaches that contribute to unifying and structuring the diverse landscape. This state-of-the-art survey presents the most relevant approaches to unifying Petri nets in a systematic and coherent way. The 14 chapters written by leading researchers are organized in topical sections on application-oriented approaches, unifying frameworks, and theoretical approaches.

✦ Table of Contents

Unifying Petri Nets
Preface
Table of Contents
''What Is a Petri Net?''
1 Introduction
2 A Graphical Notation
3 A Precise Mathematical Language
4 A Structured Set of Activities that Removehfill penalty -@M and Add Tokens
5 A Compact Way to Specify Behavior
5.1 Runs
5.2 Trees
5.3 Graphs
6 A Formalism Equipped with Analysis Methods
6.1 Simulation
6.2 Analysis
6.3 Verification
6.4 Semi-decision Methods
6.5 Proof Methods
6.6 Validation
7 A Model of a Distributed System
8 Conclusion
References
The >>Petri Net Baukasten<<: An Overview
1 Introduction
2 Petri Net Technology and the PNBaukasten
2.1 textsc {Petridiscretionary {-}{}{}netz-Techdiscretionary {-}{}{}nodiscretionary {-}{}{}lodiscretionary {-}{}{}gie}xspace
2.2 The PNBaukasten
2.3 Common Base
2.4 Application Developer View
2.5 Expert View
2.6 Tool Developer View
2.7 Relation of Common Base with Views
2.8 Petri Net Techniques in the PNBaukasten
3 Common Base
4 Application Developer Viewxspace
5 The Expert Viewxspace
6 Tool Developer Viewxspace
7 Conclusion: Installment, Maintenance, and Evolution of the PNBaukasten
References
1 Appendix
1.1 Formal Petri Net Techniques
1.2 Abstract Petri Net Frames
1.3 Actualization
1.4 Transformations
Improving the Usability of Petri Nets with the >>Petri Net Baukasten<<
1 Introduction
2 The Common Basexspace of the frqq Petri Net Baukastenflqq xspace
2.1 Object-Oriented Description
2.2 Construction of the Petri Net Classification
2.3 The Structural Model of the Common Basexspace
3 Assisted Application Development
3.1 Notions
3.2 Objectives
3.3 Use Cases
4 Application Developer Viewxspace
4.1 The Structural Model
4.2 Relation to the Common Basexspace
4.3 Relation to the Tool Developer Viewxspace
5 An Assistance System for the Application Developer
5.1 Architecture of the Assistance System
5.2 Structural Model of the Repository
6 Conclusion
References
Implementation of Parameterized Net Classes with the Petri Net Kernel of the >>Petri Net Baukasten<<
1 Introduction
2 Introduction to Parameterized Net Classes
3 The Petri Net Kernel
4 Implementing Parameterized Net Classes
5 Conclusion and Outlook
References
Process Landscaping: Modelling Distributed Processes and Proving Properties of Distributed Process Models
1 Introduction
2 Attributes Describing Distribution Properties of a Process Landscape
3 Formalization and Analysis of Process Landscapes in PLL
3.1 PLL (Process Landscaping Language)
3.2 Graphical Notation of PLL Elements
4 Formalization and Analysis of Process Landscapes in Petri Net Notation
4.1 Mapping PLL to Petri Net Notation
4.2 Analysis Example of a Process Landscape in Petri Net Representation
5 Conclusion
References
Petri Nets over Partial Algebra
1 Introduction
2 Mathematical Preliminaries
3 The General Approach
4 Elementary Nets
5 Elementary Nets with Positive Context
6 Elementary Nets with Negative Context
7 Elementary Nets with Mixed Context
8 Relationship between Process Terms and Processes hfill penalty -@M of Elementary Nets with Context
8.1 Process Semantics of Elementary Nets with Context
8.2 Compositionality of Processes
8.3 Relationship between Process Terms and Processeshfill penalty -@M of Elementary Nets with Context
9 Place/Transition Nets
9.1 Place/Transition Nets with Inhibitor Arcs
9.2 Nets with Capacities
10 Conclusion
References
Parameterized Net Classes: A Uniform Approach to Petri Net Classes
1 Introduction
2 Set-Theoretical Approach o Parameterized Net Classes
2.1 Relevance of Parameters for Net Classes
2.2 Algebraic Presentation of Place/Transition Nets
2.3 Algebraic Presentation of Elementary Nets
2.4 Variants of Net Classes
2.5 Mathematical Notation of Parameters for Net Classes
3 Categorical Approach to Parameterized Net Classes
3.1 Introduction to Categorical Concepts
3.2 Morphisms of Place/Transition Nets
3.3 Benefits of Morphisms for Petri Nets
3.4 Parameters of Net Classes Based on Functors
3.5 Uniform Constructions and Results
4 Applications of Parameterized Net Classes
4.1 Requirements Engineering for a Medical Information cite {pEPE96}
4.2 Developing a Model of an Elevator cite {pPGH99}
5 Low-Level Abstract Petri Nets
6 The Data Type Formalism Parameter
6.1 Specification Frames as the Data Type Formalism
7 High-Level Abstract Petri Nets
7.1 Basic Notions of High-Level Abstract Petri Nets
7.2 Instances of High-Level Abstract Petri Nets
8 Structuring Results for Abstract Petri Nets
8.1 Rule-Based Refinement
8.2 Local Confluence and Parallelism for Rule-Based Refinement
8.3 Horizontal Structuring and Its Compatibilityhfill penalty -@M with Rule-Based Refinement
9 Conclusion
References
1 Review of High-Level Replacement Systems
1.1 High-Level Replacement System and HLR-Conditions
1.2 ensuremath {cal Q}-Conditions
2 Proofs of the Main Results
2.1 Proofs of Theorem ref {th.fir.mor.llapn} and Theorem ref {th.morprefire}
2.2 Proof of Theorem ref {th.cocomplete}
2.3 Proofs of Theorems Concerning Rule-Based Refinement
Behavior and Realization Construction for Petri Nets Based on Free Monoid and Power Set Graphs
1 Introduction
2 Place/Transition Nets and Free Monoid Graphs
3 The Behavior and Realization Problem for Petri Nets in a Categorical Framework
4 Behavior and Realization of Place/Transition Nets and Elementary Nets
4.1 Place/Transition Nets as M-netspacefactor @m xspace {s}
4.2 Construction of the Marking Graph of Place/Transition Nets
4.3 Realizable Free Monoid Graphs
4.4 PT-G netspacefactor @m xspace {s} as M-netspacefactor @m xspace {s}
4.5 Main Results for Specific Place/Transition Nets
4.6 Specific Elementary Nets as M-netspacefactor @m xspace {s}
4.7 Elementary Nets with Loopsspacefactor @m xspace
4.8 Unsafe Elementary Nets
4.9 Main Results for Specfic Elementary Nets
4.10 Summary (Applications of M-netspacefactor @m xspace {s} and F-graphspacefactor @m xspace {s})
5 Comparison of Constructions for Elementary Nets and Elementary Transition Systems
6 Conclusion
References
Rewriting Logic as a Unifying Framework for Petri Nets
1 Introduction
2 Preliminaries
2.1 Membership Equational Logic
2.2 Rewriting Logic
3 Place/Transition Nets
3.1 Rewriting Semantics: An Example
3.2 Rewriting Semantics in the General Case
3.3 Petri Nets with Test Arcs
4 High-Level Petri Nets
4.1 Colored Nets and Colored Net Specifications
4.2 Algebraic Net Specifications
4.3 A Case Study
4.4 Rewriting Semantics in the General Case
4.5 Execution of Algebraic Net Specifications
5 Timed Petri Nets
5.1 Interval Timed Petri Nets
5.2 Representing ITPNs in Rewriting Logic
6 Conclusions
References
Generalized Automata and Their Net Representations
1 Preliminaries
2 Objectives
3 Schizophrenic Objects and Dual Adjunctions
3.1 Dual Adjunctions Induced by Schizophrenic Objects
3.2 Galois Connections
4 $Delta $-Parameterized Transition Systems and Nets
4.1 Hybrid Petri Nets
4.2 Coloured Petri Nets
4.3 Vector Addition Systems with States
4.4 $Delta $-Parameterized Transition Systems
4.5 Parameterized Nets and Their State Graphs
4.6 State Graphs as Duals of Nets
4.7 Synthesized Nets as Duals of Systems of $Delta $-Transitions
4.8 Galois Connection Derived from the Dual Adjunctionhfill penalty -@M Using Separation Axioms
4.9 Order Theoretic Galois Connection between $Delta $-Automatahfill penalty -@M and Net Systems
5 Nets with Complex Transitions
5.1 Complex Actions of Petri Nets
5.2 Concurrent Inhibitor C/E-Nets
5.3 $(Sigma ,E)$-Transition Systems and $(Sigma ,E)$-Nets
5.4 Order Theoretic Galois Connection
6 Conclusion
References
On Concurrent Realization of Reactive Systems and Their Morphisms
1 Introduction
2 Why Should We Care about Morphisms
2.1 Reactive Systems, Their Categories and Properties
2.2 A Simple Language of Modal Properties
3 Concurrent Realizations of Reactive Systems
3.1 Asynchronous Systems
3.2 (Labelled) Petri Nets
3.3 Morphisms of (Labelled) Petri Nets
3.4 Comparison with Winskel's Definition
3.5 Properties of Case Graph Functor
3.6 Labelled Petri Nets as Concurrent Realizationshfill penalty -@M of Reactive Systems
4 Concurrent Realizations hfill penalty -@M of Concrete Asynchronous Systems
4.1 Concrete Asynchronous Systems
4.2 Concrete Asynchronous Systems Revisited
4.3 Comparison with Elementary Transition Systems
4.4 Labelled Safe Petri Nets and Their Products
4.5 Towards a Functorial Realization of Concrete Asynchronous Systems by Means of Labelled Safe Petri Nets
5 Examples, Conclusions and Further Work
5.1 Mandala
5.2 Realization of the Emerson-Clarke Scheduler
5.3 Zig-zag Morphism and Systematic Refinementhfill penalty -@M of Concrete Asynchronous Systems
5.4 Further Research
References
Transactions and Zero-Safe Nets*
Introduction
1 Place/Transition Petri Nets
1.1 Petri Nets Are Monoids
2 Zero-Safe Nets
2.1 Introductory Example: Dining Philosophers
2.2 textsf {textsl {CTph}} vs. textsf {textsl {ITph}}: The Multicasting System Example
2.3 Collective Token Approach
2.4 Individual Token Approach
2.5 One More Example
3 Translation of Languages with Synchronization Primitives
3.1 Distributed Sum
4 An Operational Definition for Transactions
4.1 relax mathversion {bold}{sc pt} Net Unfolding
4.2 relax mathversion {bold}{sc zs} Net Unfolding
5 Zero-Safe Nets and Read Arcs
5.1 Contextual Nets
5.2 Zero-Safe Contextual Nets
5.3 A Distributed Contextual Interpreter
References
Two Algebraic Process Semantics for Contextual Nets
Introduction
1 Preliminaries
1.1 Contextual Nets
1.2 Petri Nets Are Monoids
2 Collective Contexts
3 Individual Contexts
References
Continuous Petri Nets and Transition Systems
1 Introduction
2 Control Paths
3 Continuous Petri Nets and Concurrency
4 Continuous Automata with Concurrency; the Functors $an$ and $na$
5 An Adjunction
6 A Coreflection
7 Products and Coproducts
8 Conclusion
References
Author Index