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## Fairness for Non-Interleaving Concurrency

### Abstract

Fairness in a non-interleaving semantic model for concurrency has been investigated. In contrast to the interleaving approach, which reduces non-sequential behaviours to a nondeterministic choice between possible interleavings of activities of concurrent processes, concurrency and causality were assumed as primitive notions. Mazurkiewicz's trace languages were chosen as behavioural representations of systems and Shields' asynchronous transition systems as their acceptors. The notion central to these two formalisms is one of causal independency, which determines trace equivalence (congruence) in the monoid of strings. Equivalence classes of strings are called traces.\ud The quotient monoid of traces forms a poset with trace prefix ordering.\ud First, trace languages have been enhanced to allow for infmite traces; this was achieved by introducing trace preorder relation on possibly infinite strings. It has been shown that the extension gives rise to the domain of traces and an infinitary monoid, which specializes to the domain and the infinitary monoid of strings of Nivat's, Asynchronous transition systems have been equipped with a notion of a process structure; a variety of process structures ordered by refinement relation are possible for a given system. Each process structure determines projective preorder and equivalence relations in the monoid of strings, which are shown to coincide with the trace preorder and trace equivalence.\ud In this setting, a topological characterization of behavioural properties which includes safety, progress and fairness properties has been provided. Fairness properties form a subclass of infinitary progress properties that is closed under arbitrary union.\ud Unconditional process fairness properties that are determined by process structures have been distinguished; they form a lattice with inclusion ordering. Finally, strength predicates were incorporated to allow for a variety of specific fairness properties such as weak and strong process fairness as well as equifairness and state fairness

Publisher: University of Leicester
Year: 1989
OAI identifier: oai:lra.le.ac.uk:2381/8809

### Citations

1. (1980). A calculus for communicating systems,
2. (1980). A Compendium (~fContinuous Lattices,
3. (1986). A Complete Rule for Equifair Termination,
4. (1976). A Discipline ofprogramming,
5. (1984). A Fair Calculus of Communicating Systems,
6. (1982). A Powerdomain for Countable Non-determinism, in:
7. (1979). A Survey of Fairness Notions, to appear III
8. (1984). A Theory of Communicating Sequential Processes,
9. (1986). Algebra of communicating processes, in:
10. (1987). An Algebraic Theory of Fair Asynchronous Communicating Processes,
11. (1981). An axiomatic definition of synchronisation primitives,
12. (1976). An Axiomatic Proof Technique for Parallel Programs,
13. (1987). An Introduction to the Regular Theory of Fairness,
14. (1988). Analysing infinitely branching transition systems,
15. (1988). Another View of 'Fairness',
16. (1986). Applications of temporal logic to the specification and verification of reactive systems: a survey of current trends, in:
17. (1987). Appraising Fairness in Languages for Distributed Programming, in:
18. (1988). Basic Notions of Trace Theory, in: REX School/Workshop on Linear Time, Branching time and Partial Order in Logics and Models for Concurrency (Nordwijkerhout,
19. (1988). Behavioural Presentation, in: REX Schooltworkshop on Linear Time, Branching time and Partial Order in Logics and Models for Concurrency (Nordwijkerhout,
20. (1986). Bounded non-determinism and induction principle in process algebra,
21. (1984). Communicating Sequential Processes,
22. (1981). Concurrency and Automata on Infinite Sequences, in:
23. (1977). Concurrent Program Schemes and Their Interpretations,
24. (1985). Defining Liveness,
25. (1977). Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory,
26. (1983). Domains and Predicate Transformers, a topological view, in:
27. (1988). Event Fairness in Asynchronous Transition Systems,
28. (1986). Event Structures,
29. (1986). Fair Processes, in:
30. (1984). Fairness and Conspiracies,
31. (1983). Fairness and Related Properties in Transition Systems - A Temporal Logic to Deal with Fairness,
32. (1985). Fairness Properties in Process Algebra with Applications in Communication Protocol Verification.
33. (1976). Formal Verification of Parallel Programs,
34. (1987). Grumberg 0.,
35. (1981). Impartiality, Justice and Fairness: The Ethics of Concurrent Termination, in:
36. (1987). in:
37. (1987). Infinite Streams and Finite Observations in the Semantics of Uniform Concurrency,
38. (1988). Modelling Concurrency Using Ambiguous Asynchronous Transition Systems,
39. (1983). Modelling Finite Delay Operators,
40. (1984). Modelling the distributed termination convention in esp,
41. (1987). Models for Parallelism.
42. (1960). Naive Set Theory,
43. (1985). Nets, An Introduction,
44. (1986). nets: basic notions, structure, behaviour, in: Current Trends
45. (1987). Non-Interleaving Semantic Model for NonDeterministic Concurrent Processes,
46. (1984). Now You May Compose Temporal Logic Specifications, in:
47. (1983). On the extremely fair treatment of probabilistic algorithms, in:
48. (1979). On the Semantics of Fair Parallelism, in: Abstract Software Specifications,
49. (1980). On the Temporal Analysis of Fairness, in:
50. (1988). Operational and Algebraic Semantics of Concurrent Processes,
51. (1969). Parallel Program Schemata,
52. (1988). Permutation of transitions: an event structure semantics for CCS and SCCS, in: REX School/Workshop on Linear Time, Branching time and Partial Order in Logics and Models for Concurrency (Nordwijkerhout,
53. (1988). Position Paper on Fairness,
54. (1987). Proof of specification properties by using finite state machines and temporal logic, in:
55. (1975). Proving Assertions about Parallel Programs,
56. (1982). Proving Liveness Properties of Concurrent Programs,
57. (1977). Proving the Correctness of Multiprocess Programs,
58. (1984). Semantics of Concurrent Systems: A Modular FixedPoint Trace Approach, in:
59. (1987). Semantique Asynchrone et Comportements Infini en CSP,
60. (1986). Sometimes' and 'Not Never' Revisited: On Branching versus Linear Time Temporal Logic,
61. (1981). Temporal verification of concurrent programs,
62. (1988). Theory of Traces,
63. (1984). Traces, Ilistories, Graphs: Instances of a Process Monoid, in:
64. (1984). Transformations Realizing Fairness Assumptions for Parallel Programs, in:
65. (1983). Verification of fairness in an implementation of monitors, in:
66. (1986). Verification of multiprocess probabilistic protocols,
67. (1987). Weak and Strong Fairness in CCS,

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