This volume provides an elementary introduction to Communicating Sequential Processes (CSP) and its use as a formal method for understanding concurrency. Examples and exercises are presented throughout to aid teaching and to help motivate students studying this difficult subject.

Preface ix Acknowledgements xv Part 1 The language of CSP 1 Sequential processes 3 1.1 Events and processes 3 1.2 Performing events 8 1.3 Recursion 13 1.4 Choice 20 2 Concurrency 31 2.1 Alphabetized parallel 31 2.2 Interleaving 44 2.3 Interface parallel 50 3 Abstraction and control flow 55 3.1 Hiding 55 3.2 Event renaming 62 3.3 Sequential composition 69 3.4 Interrupt 72 3.5 Notes 74 Part II Analysing processes 4 Traces 87 4.1 Sequences 87 4.2 Trace semantics 91 4.3 Recursion 117 4.4 Testing 133 4.5 Congruence 136 5 Specification and verification with traces 141 5.1 Property-oriented Specification 141 5.2 Verification 143 5.3 Recursion induction 155 5.4 Case study: Distributed sum 160 5.5 Process-oriented specification 168 6 Stable failures 173 6.1 Observing processes 174 6.2 Process semantics 178 6.3 Recursion 188 7 Specification and verification with failures 195 7.1 Property-oriented specification 195 7.2 Verification 197 7.3 Recursion induction 206 7.4 Process-oriented specification 209 7.5 Case study: Distributed sum 212 8 Failures, divergences, and infinite traces 221 8.1 Observing processes 221 8.2 Process semantics 229 8.3 Recursion 242 8.4 Specification and verification 248 8.5 Recursion induction 253 8.6 Case study: Distributed sum 256 8.7 Must testing and FDI equivalence 257 8.8 Notes 258 Part III Introducing time 9 The timed language 267 9.1 Timed computational model 268 9.2 Transitions 269 9.3 Performing events 270 9.4 Choice 275 9.5 Recursion 286 9.6 Concurrency 290 9.7 Abstraction 297 9.8 Flow of control 304 10 Timed transition systems 313 10.1 Evolution 313 10.2 Executions 315 10.3 Well-timed processes 327 10.4 Notes 329 Part IV Timed analysis 11 Semantics of timed CSP 335 11.1 Timed observations 336 11.2 Timed failures semantics 347 11.3 Recursion 358 11.4 Testing and timed failures equivalence 363 12 Timed specification and verification 369 12.1 Specification 369 12.2 Verification 375 12.3 Recursion induction 385 12.4 Ill-timed processes 388 12.5 Case study: Fischer’s protocol 390 13 Timewise refinement 399 13.1 Trace timewise refinement 400 13.2 Failures timewise refinement 410 13.3 Refinement and parallel composition 413 13.4 Case study: a railway crossing 431 13.5 FDI timewise refinement 436 13.6 Testing and timewise refinement 439 13.7 Notes 442 Appendix A: Event-based time 447 A.1 Standard CSP and took 448 A.2 Translating from timed CSP 454 A.3 Notes 465 Appendix B: Model-checking with FDR 469 B.1 Interacting with FDR 470 B.2 How FDR checks refinement 473 B.3 Machine readable CSP 478 References 485 Notation 493 Index 498 Index of Processes 507

The CSP approach has been widely used in the specification, analysis and verification of concurrent and real-time systems, and for understanding the particular issues that can arise when concurrency is present. It provides a language which enables specifications and designs to be clearly expressed and understood, together with a supporting theory which allows them to be analysed and shown to be correct. This book supports advanced level courses on concurrency covering timed and untimed CSP. The first half introduces the language of CSP, the primary semantic models (traces, failures, divergences and infinite traces), and their use in the modelling, analysis and verification of concurrent systems. The second half of the book introduces time into the language, brings in the timed semantic model (timed failures) and finally presents the theory of timewise refinement which links the two halves together. Author's Website containing: * Exercises and solutions * Instructor's resources * Example CSP programs to run on FDR and ProBe * Links to useful sites

THE LANGUAGE OF CSP. Sequential Processes. Concurrency. Abstraction and Control Flow. ANALYSING PROCESSES. Traces. Specification and Verification with Traces. Stable Failures. Specification and Verification with Failures. Failures, Divergences, and Infinite Traces. INTRODUCING TIME. The Timed Language. Timed Transition Systems. TIMED ANALYSIS. Semantics of Timed CSP. Timed Specification and Verification. Timewise Refinement. Appendices. References. Notation. Indexes.