Process Algebra With Timing

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Format: Hardcover
Pub. Date: 2002-09-01
Publisher(s): Springer-Verlag New York Inc
List Price: $119.99

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Summary

Timing issues are of growing importance for the conceptualization and design of computer-based systems. Timing may simply be essential for the correct behaviour of a system, e.g. of a controller. Even if timing is not essential for the correct behaviour of a system, there may be good reasons to introduce it in such a way that suitable timing becomes relevant for the correct behaviour of a complex system. This book is unique in presenting four algebraic theories about processes, each dealing with timing from a different point of view, in a coherent and systematic way. The timing of actions is either relative or absolute and the underlying time scale is either discrete or continuous. All presented theories are extensions of the algebra of communicating processes. The book is essential reading for researchers and advanced students interested in timing issues in the context of the design and analysis of concurrent and communicating processes.

Table of Contents

Preface v
No Timing
1(30)
Basic Process Algebra
1(17)
Basic Concepts
2(7)
The Theories BPA and BPAδ
9(4)
BPA with Recursion
13(5)
Algebra of Communicating Processes
18(13)
Additional Concepts
19(3)
The Theory ACP
22(5)
ACP with Recursion
27(1)
Some Calculations: Message-Passing System
28(2)
Postlude
30(1)
Discrete Relative Timing
31(40)
Basic Process Algebra
32(21)
Basic Concepts
32(7)
The Theory BPAdrt-ID
39(4)
BPAdrt-ID with Recursion
43(3)
The Theory BPAdrt
46(3)
BPAdrt with Recursion
49(1)
The Theory BPAdrt
49(4)
BPAdrt with Recursion
53(1)
Algebra of Communicating Processes
53(15)
Additional Concepts
54(4)
The Theory ACPdrt
58(5)
ACPdrt with Recursion
63(1)
Some Calculations: PAR Protocol
64(3)
Postlude
67(1)
Connections
68(3)
Relating ACPdrt to ACP
68(1)
Relative Timing versus Absolute Timing
69(2)
Discrete Absolute Timing
71(52)
Basic Process Algebra
72(15)
Basic Concepts
72(5)
The Theory BPAdat
77(6)
BPAdat with Recursion
83(4)
Algebra of Communicating Processes
87(18)
Additional Concepts
87(4)
The Theory ACPdat
91(5)
ACPdat with Recursion
96(1)
Some Calculations: Fischer's Protocol
97(6)
Postlude
103(2)
Discrete Initial Abstraction
105(7)
Additional Concepts
105(3)
The Theory ACPdat
108(3)
Discussion
111(1)
Time-Dependent Conditions
112(5)
Additional Concepts
112(2)
The Theory ACPdat C
114(3)
Connections
117(6)
Relating ACPdat to ACP
117(1)
Relating ACPdat to ACPdrt and ACPdat
118(2)
Time-Stamped Actions
120(1)
Discrete Time versus Continuous Time
121(2)
Continuous Relative Timing
123(36)
Basic Process Algebra
124(17)
Basic Concepts
124(6)
The Theory BPAsrt
130(5)
BPAsrt with Recursion
135(2)
BPAsrt with Integration
137(4)
Algebra of Communicating Processes
141(14)
Additional Concepts
141(3)
The Theory ACPsrt
144(5)
ACPsrt with Recursion
149(1)
ACPsrt with Integration
149(4)
Example: Bottle Filling System
153(2)
Connections
155(4)
Relating ACPsrt I to ACP
155(1)
Relating ACPsrt I to ACPdrt
155(1)
Generalized Relative Delay
156(3)
Continuous Absolute Timing
159(46)
Basic Process Algebra
159(17)
Basic Concepts
160(5)
The Theory BPAsat
165(5)
BPAsat with Recursion
170(3)
BPAsat with Integration
173(3)
Algebra of Communicating Processes
176(16)
Additional Concepts
176(3)
The Theory ACPsat
179(5)
ACPsat with Recursion
184(1)
ACPsat with Integration
184(3)
Example: Railroad Crossing System
187(3)
Postlude
190(2)
Standard Initial Abstraction
192(3)
Additional Concepts
192(1)
The Theory ACPsat I
193(2)
Time-Dependent Conditions
195(5)
Additional Concepts
196(1)
The Theory ACPsatIC
197(3)
Connections
200(5)
Relating ACPsatI to ACP
201(1)
Relating ACPsatI to ACPsrtI and ACPsatI
201(1)
Relating ACPsatI to CPdat
202(3)
Abstraction
205(26)
No Timing
205(3)
Discrete Relative Timing
208(9)
Basic Process Algebra
209(3)
Algebra of Communicating Processes
212(2)
Some Calculations
214(3)
Relating ACPdrtτ to ACPτ
217(1)
Discrete Absolute Timing
217(4)
Basic Process Algebra
218(1)
Algebra of Communicating Processes
219(1)
Some Calculations
220(1)
Relating ACPτdat to ACPτ
221(1)
Continuous Relative Timing
221(5)
Basic Process Algebra
221(3)
Algebra of Communicating Processes
224(1)
Relating ACPτsrt to ACPτ
225(1)
Continuous Absolute Timing
226(5)
Basic Process Algebra
226(1)
Algebra of Communicating Processes
227(1)
Some Calculations
228(2)
Relating ACPτsat to ACPτ
230(1)
Features
231(10)
State Operator
232(3)
Maximal Progress
235(2)
Process Creation
237(4)
A. Soundness and Completeness of ACPdrt 241(10)
Elimination
241(2)
Soundness
243(5)
Completeness
248(3)
B. Background Material 251(24)
Basic Equational Logic and SOS Theory
251(10)
Equational Logic
251(5)
SOS Theory
256(5)
Some Further Topics
261(9)
TSSs with Negative Premises
262(1)
Variable Binding Operators
263(3)
Conservativity and Completeness
266(1)
Generalizations
267(1)
Given Sorts and Parametrization
268(2)
Non-negative Real Numbers
270(5)
References 275(4)
Glossary 279(6)
Index 285

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