Petri Net Algebra,9783540673989

Petri Net Algebra

by ; ;
ISBN13: 9783540673989
ISBN10: 3540673989
Format: Hardcover
Pub. Date: 2001-03-01
Publisher(s): Springer-Verlag New York Inc
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Summary

This book presents a step-by-step development of a rigorous framework for the specification and verification of concurrent systems. Petri Net Algebra takes its inspiration and methods from Process Algebra and Petri Nets, two prominent branches of concurrency theory. Added synergistic benefit is derived from combining their respective advantages. Petri nets are treated as composable objects, and as such they are embedded in a general process algebra. On the other hand, a generic process algebra is given an automatic Petri net semantics so that net-based verification techniques, based on structural invariants and causal partial orders, can be applied to the process algebra. The book contains full proofs, carefully chosen examples and several possible directions for further research. A unique aspect is that the development of the Petri net algebra is handled so as to allow for further application-oriented extensions and modifications.

Table of Contents

Introduction
1(7)
The Petri Box Calculus
7(22)
An Informal Introduction to CCS
8(1)
An Informal Introduction to Petri Nets
9(2)
The Structure and Behaviour of PBC Expressions
11(3)
Sequential Composition
14(1)
Synchronisation
15(6)
Synchronisation and Parallel Composition
21(3)
Other PBC Operators
24(1)
Modelling a Concurrent Programming Language
25(3)
Literature and Background
28(1)
Syntax and Operational Semantics
29(44)
Standard PBC Syntax
29(4)
Structured Operational Semantics
33(29)
The Basic Setup
35(2)
Equivalence Notions
37(4)
Elementary Actions
41(1)
Parallel Composition
42(3)
Choice Composition
45(1)
Sequential Composition
46(1)
Synchronisation
47(1)
Standard PBC Synchronisation
47(3)
Auto-synchronisation and Multilink-synchronisation
50(2)
Step-synchronisation
52(1)
Basic Relabelling
53(1)
Restriction
54(1)
Scoping
55(3)
Iteration
58(1)
Recursion
59(3)
Extensions
62(7)
Generalised Iterations
62(2)
Data Variables
64(2)
Generalised Control Flow Operators
66(1)
Generalised Communication Interface Operators
67(2)
Extended PBC Syntax
69(1)
Examples of Transition Systems
69(2)
Literature and Background
71(2)
Petri Net Semantics
73(60)
Compositionality and Nets
73(2)
Labelled Nets and Boxes
75(15)
An Example
75(1)
Actions and Relabellings
76(1)
Labelled Nets
77(5)
Equivalence Notions
82(4)
Boxes
86(4)
Net Refinement
90(14)
Operator Boxes
90(2)
Intuition Behind Net Refinement
92(3)
Place and Transition Names
95(2)
Formal Definition of Net Refinement
97(2)
Remarks on Net Refinement
99(2)
Properties
101(2)
Discussion
103(1)
Petri Net Semantics of PBC
104(25)
Elementary Actions
106(1)
Parallel Composition
106(1)
Choice Composition
107(2)
Sequential Composition
109(1)
Basic Relabelling
110(1)
Synchronisation
110(9)
Restriction
119(1)
Scoping
120(1)
Iteration
120(3)
Data Variables
123(1)
Generalised Control Flow Operators
124(2)
Generalised Communication Interface Operators
126(1)
Generalised Iterations
127(2)
Refined Operators
129(3)
Literature and Background
132(1)
Adding Recursion
133(40)
Inclusion Order on Labelled Nets
133(2)
Solving Recursive Equations
135(22)
Using Fixpoints to Solve Recursive Equations
137(3)
Places and Transitions in Net Solutions
140(4)
An Example of the Limit Construction
144(1)
Deriving Seed Boxes
145(6)
A Closed Form of the Maximal Solution
151(2)
Minimal Solutions
153(4)
Finitary Equations and Finite Operator Boxes
157(4)
Finitary Equation
157(2)
Finite Operator Box
159(2)
Further Examples
161(6)
Unbounded Parallel Composition
161(1)
Rear-unguardedness
162(2)
Concurrency Within Unbounded Choice
164(2)
Extreme Unguardedness
166(1)
(Non)use of Empty Nets in the Limit Construction
167(1)
Solving Systems of Recursive Equations
167(5)
Approximations, Existence, and Uniqueness
168(1)
A Closed Form of the Maximal Solution
169(2)
Guarded Systems
171(1)
Literature and Background
172(1)
S-invariants
173(54)
S-invariants, S-components, and S-aggregates
174(9)
S-invariants
176(5)
S-components
181(1)
S-aggregates
182(1)
The Synthesis Problem for Net Refinement
183(17)
Composing S-invariants
185(5)
Multiplicative Distribution Functions
190(3)
Ex-binary S-invariants
193(2)
Rational Groupings
195(5)
The Synthesis Problem for Recursive Systems
200(16)
Name Trees of Nets in the Maximal Solution
201(1)
Composing S-invariants for Recursive Boxes
202(7)
Coverability Results
209(7)
Finite Precedence Properties
216(10)
Process Semantics
218(4)
Finite Precedence of Events
222(3)
Finiteness of Complete Processes
225(1)
Literature and Background
226(1)
The Box Algebra
227(68)
SOS-operator Boxes
227(14)
A Running Example
232(1)
Properties of Factorisations
232(2)
The Domain of Application of an SOS-operator Box
234(1)
Static Properties of Refinements
235(4)
Markings of Nets
239(2)
Structured Operational Semantics of Composite Boxes
241(18)
Soundness
243(2)
Similarity Relation on Tuples of Boxes
245(3)
Completeness
248(5)
Solutions of Recursive Systems
253(2)
Behavioural Restrictions
255(4)
A Process Algebra and its Semantics
259(35)
A Running Example: the DIY Algebra
262(2)
Infinite Operators
264(3)
Denotational Semantics
267(3)
Structural Similarity Relation on Expressions
270(9)
Transition-based Operational Semantics
279(7)
Consistency of the Two Semantics
286(1)
Label-based Operational Semantics
287(3)
Partial Order Semantics of Box Expressions
290(4)
Literature and Background
294(1)
PBC and Other Process Algebras
295(18)
(Generalised) PBC is a Box Algebra
295(13)
PBC Without Loops
295(4)
Safe Translation of the Ternary PBC Iteration
299(7)
PBC with Generalised Loops
306(2)
Other Process Algebras
308(4)
CCS
310(1)
TCSP
311(1)
COSY
311(1)
Literature and Background
312(1)
A Concurrent Programming Language
313(36)
Syntax of Razor
313(5)
Programs and Blocks
315(1)
Declarations
315(1)
Commands and Actions
316(1)
Guarded Commands
316(1)
Expressions and Operators
317(1)
Syntactic Variations
317(1)
Semantics of Razor
318(11)
Programs, Blocks, and Declarations
319(2)
Basic Channel Processes
321(3)
Command Connectives
324(1)
Actions and Guarded Commands
325(4)
Three Razor Programs
329(3)
Adding Recursive Procedures
332(4)
Some Consequences of the Theory
336(4)
Proofs of Distributed Algorithms
340(7)
A Final Set of Petri-Net-Related Definitions
340(2)
Peterson's Mutual Exclusion Algorithm
342(4)
Dekker's and Morris's Mutual Exclusion Algorithms
346(1)
Literature and Background
347(2)
Conclusion
349(2)
Appendix: Solutions of Selected Exercises 351(11)
References 362(7)
Index 369

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