Algebraic Theory for True Concurrency presents readers with the algebraic laws for true concurrency. Parallelism and concurrency are two of the core concepts within computer science. This book covers the different realms of concurrency, which enables programs, algorithms or problems to be broken out into order-independent or partially ordered components to improve computation and execution speed. There are two primary approaches for executing concurrency: interleaving concurrency and true concurrency. The main representative of interleaving concurrency is bisimulation/rooted branching bisimulation equivalences which is also readily explored.
This work eventually founded the comprehensive axiomatization modulo bisimulation equivalence -- ACP (Algebra of Communicating Processes).The other approach to concurrency is true concurrency. Research on true concurrency is active and includes many emerging applications. First, there are several truly concurrent bisimulation equivalences, including: pomset bisimulation equivalence, step bisimulation equivalence, history-preserving (hp-) bisimulation equivalence, and hereditary history-preserving (hhp-) bisimulation equivalence, the most well-known truly concurrent bisimulation equivalence.
1. 1. Introduction - p. 1 2. 2. Backgrounds - p. 7 3. 3. A calculus for true concurrency - p. 15 4. Abstract - p. 15 5. 3.1 Syntax and operational semantics - p. 15 6. 3.2 Strongly truly concurrent bisimulations - p. 18 7. 3.3 Weakly truly concurrent bisimulations - p. 38 8. 3.4 Applications - p. 44 9. 3.5 Conclusions - p. 46 10. References - p. 47 11. 4. Algebraic laws for true concurrency - p. 49 12. Abstract - p. 49 13. 4.1 Basic algebra for true concurrency - p. 49 14. 4.2 Algebra for parallelism in true concurrency - p. 70 15. 4.3 Recursion - p. 101 16. 4.4 Abstraction - p. 113 17. 4.5 Applications - p. 129 18. 4.6 Extensions - p. 133 19. 4.7 Axiomatization for hhp-bisimilarity - p. 151 20. 4.8 Conclusions - p. 158 21. References - p. 158 22. 5. Mobility - p. 159 23. Abstract - p. 159 24. 5.1 Syntax and operational semantics - p. 159 25. 5.2 Strongly truly concurrent bisimilarities - p. 162 26. 5.3 Algebraic theory - p. 177 27. 5.4 Conclusions - p. 179 28. References - p. 179 29. 6. Guards - p. 181 30. Abstract - p. 181 31. 6.1 Operational semantics - p. 181 32. 6.2 BATCBATC with guards - p. 183 33. 6.3 APTCAPTC with guards - p. 188 34. 6.4 Recursion - p. 198 35. 6.5 Abstraction - p. 201 36. 6.6 Hoare logic for APTCGAPTCG - p. 209 37. 6.7 Conclusions - p. 212 38. References - p. 212 39. References - p. 213 40. Index - p. 215
Algebraic Theory for True Concurrency presents readers with the algebraic laws for true concurrency. Parallelism and concurrency are two of the core concepts within computer science. This book covers the different realms of concurrency, which enables programs, algorithms or problems to be broken out into order-independent or partially ordered components to improve computation and execution speed. There are two primary approaches for executing concurrency: interleaving concurrency and true concurrency. The main representative of interleaving concurrency is bisimulation/rooted branching bisimulation equivalences which is also readily explored.
This work eventually founded the comprehensive axiomatization modulo bisimulation equivalence -- ACP (Algebra of Communicating Processes).The other approach to concurrency is true concurrency. Research on true concurrency is active and includes many emerging applications. First, there are several truly concurrent bisimulation equivalences, including: pomset bisimulation equivalence, step bisimulation equivalence, history-preserving (hp-) bisimulation equivalence, and hereditary history-preserving (hhp-) bisimulation equivalence, the most well-known truly concurrent bisimulation equivalence.
1. 1. Introduction - p. 1 2. 2. Backgrounds - p. 7 3. 3. A calculus for true concurrency - p. 15 4. Abstract - p. 15 5. 3.1 Syntax and operational semantics - p. 15 6. 3.2 Strongly truly concurrent bisimulations - p. 18 7. 3.3 Weakly truly concurrent bisimulations - p. 38 8. 3.4 Applications - p. 44 9. 3.5 Conclusions - p. 46 10. References - p. 47 11. 4. Algebraic laws for true concurrency - p. 49 12. Abstract - p. 49 13. 4.1 Basic algebra for true concurrency - p. 49 14. 4.2 Algebra for parallelism in true concurrency - p. 70 15. 4.3 Recursion - p. 101 16. 4.4 Abstraction - p. 113 17. 4.5 Applications - p. 129 18. 4.6 Extensions - p. 133 19. 4.7 Axiomatization for hhp-bisimilarity - p. 151 20. 4.8 Conclusions - p. 158 21. References - p. 158 22. 5. Mobility - p. 159 23. Abstract - p. 159 24. 5.1 Syntax and operational semantics - p. 159 25. 5.2 Strongly truly concurrent bisimilarities - p. 162 26. 5.3 Algebraic theory - p. 177 27. 5.4 Conclusions - p. 179 28. References - p. 179 29. 6. Guards - p. 181 30. Abstract - p. 181 31. 6.1 Operational semantics - p. 181 32. 6.2 BATCBATC with guards - p. 183 33. 6.3 APTCAPTC with guards - p. 188 34. 6.4 Recursion - p. 198 35. 6.5 Abstraction - p. 201 36. 6.6 Hoare logic for APTCGAPTCG - p. 209 37. 6.7 Conclusions - p. 212 38. References - p. 212 39. References - p. 213 40. Index - p. 215
