ISBN: 354043447X
TITLE: Process Algebra with Timing
AUTHOR: Baeten, Middelburg
TOC:

Preface V
1. No Timing 1
1.1 Basic Process Algebra 1
1.1.1 Basic Concepts 2
1.1.2 The Theories BPA and BPA_delta 9
1.1.3 BPA with Recursion 13
1.2 Algebra of Communicating Processes 18
1.2.1 Additional Concepts 19
1.2.2 The Theory ACP 22
1.2.3 ACP with Recursion 27
1.2.4 Some Calculations: Message-Passing System 28
1.2.5 Postlude 30
2. Discrete Relative Timing 31
2.1 Basic Process Algebra 32
2.1.1 Basic Concepts 32
2.1.2 The Theory BPA^drt_-ID 39
2.1.3 BPA^drt_-ID with Recursion 43
2.1.4 The Theory BPA^drt_ 46
2 1 5 BPA^drt_ with Recursion 49
2.1.6 The Theory BPA^drt 49
2.1.7 BPA^drt with Recursion 53
2.2 Algebra of Communicating Processes 53
2.2.1 Additional Concepts 54
2.2.2 The Theory ACP^drt 58
2.2.3 ACP^drt with Recursion 63
2.2.4 Some Calculations: PAR Protocol 64
2.2.5 Postlude 67
2.3 Connections 68
2.3.1 Relating ACP^drt to ACP 68
2.3.2 Relative Timing versus Absolute Timing 69
3. Discrete Absolute Timing 71
3.1 Basic Process Algebra 72
3.1.1 Basic Concepts 72
3.1.2 The Theory BPA^dat 77
3.1.3 BPA^dat with Recursion 83
3.2 Algebra of Communicating Processes 87
3.2.1 Additional Concepts 87
3.2.2 The Theory ACP^dat 91
3.2.3 ACP^dat with Recursion 96
3.2.4 Some Calculations: Fischer's Protocol 97
3.2.5 Postlude 103
3.3 Discrete Initial Abstraction 105
3.3.1 Additional Concepts 105
3.3.2 The Theory ACP^dat 108
3.3.3 Discussion 111
3.4 Time-Dependent Conditions 112
3.4.1 Additional Concepts 112
3.4.2 The Theory ACP^dat \surd C 114
3.5 Connections 117
3.5.1 Relating ACP^dat to ACP 117
3.5.2 Relating ACP^dat \surd to ACP^drt and ACP^dat 118
3.5.3 Time-Stamped Actions 120
3.5.4 Discrete Time versus Continuous Time 121
4. Continuous Relative Timing 123
4.1 Basic Process Algebra 124
4.1.1 Basic Concepts 124
4.1.2 The Theory BPA^srt 130
4.1.3 BPA^srt with Recursion 135
4.1.4 BPA^srt with Integration 137
4.2 Algebra of Communicating Processes 141
4.2.1 Additional Concepts 141
4.2.2 The Theory ACP^srt 144
4.2.3 ACP^srt with Recursion 149
4.2.4 ACP^srt with Integration 149
4.2.5 Example: Bottle Filling System 153
4.3 Connections 155
4.3.1 Relating ACP^srtI to ACP 155
4.3.2 Relating ACP^srtI to ACP^drt 155
4.3.3 Generalized Relative Delay 156
5. Continuous Absolute Timing 159
5.1 Basic Process Algebra 159
5.1.1 Basic Concepts 160
5.1.2 The Theory BPA^sat 165
5.1.3 BPA^sat with Recursion 170
5.1.4 BPA^sat with Integration 173
5.2 Algebra of Communicating Processes 176
5.2.1 Additional Concepts 176
5.2.2 The Theory ACP^sat 179
5.2.3 ACP^sat with Recursion 184
5.2.4 ACP^sat with Integration 184
5.2.5 Example: Railroad Crossing System 187
5.2.6 Postlude 190
5.3 Standard Initial Abstraction 192
5.3.1 Additional Concepts 192
5.3.2 The Theory ACP^satI \surd 193
5.4 Time-Dependent Conditions 195
5.4.1 Additional Concepts 196
5.4.2 The Theory ACP^satI \surd C 197
5.5 Connections 200
5.5.1 Relating ACP^satI to ACP 201
5.5.2 Relating ACP^satI \surd to ACP^srtI and ACP^satI 201
5.5.3 Relating ACP^satI \surd to ACP^dat \surd 202
6. Abstraction 205
6.1 No Timing 205
6.2 Discrete Relative Timing 208
6.2.1 Basic Process Algebra 209
6.2.2 Algebra of Communicating Processes 212
6.2.3 Some Calkulations 214
6.2.4 Relating ACP^drt_tau to ACP 217
6.3 Discrete Absolute Timing 217
6.3.1 Basic Process Algebra 218
6.3.2 Algebra of Communicating Processes 219
6.3.3 Some Calculations 220
6.3.4 Relating ACP^dat_tau to ACP 221
6.4 Continuous Relative Timing 221
6.4.1 Basic Process Algebra 221
6.4.2 Algebra of Communicating Processes 224
6.4.3 Relating ACP^srt_tau to ACP 225
6.5 Continuous Absolute Timing 226
6.5.1 Basic Process Algebra 226
6.5.2 Algebra of Communicating Processes 227
6.5.3 Some Calculations 228
6.5.4 Relating ACP^sat_tau to ACP^tau 230
7. Features 231
7.1 State Operator 232
7.2 Maximal Progress 235
7.3 Process Creation 237
A. Soundness and Completeness of ACP^drt 241
A.1 Elimination 241
A.2 Soundness 243
A.3 Completeness 248
B. Background Material 251
B.1 Basic Equational Logic and SOS Theory 251
B.1.1 Equational Logic 251
B.1.2 SOS Theory 256
B.2 Some Further Topics 261
B.2.1 TSSs with Negative Premises 262
B.2.2 Variable Binding Operators 263
B.2.3 Conservativity and Completeness 266
B.2.4 Generalizations 267
B.2.5 Given Sorts and Parametrization 268
B.3 Non-negative Real Numbers 270
References 275
Glossary 279
Index 285
END
