0 Introduction.- 0.1 Motivation and Background.- 0.2 A Taxonomy of Fairness Concepts.- 0.3 The Language of Guarded Commands (GC).- 0.3.1 A partial-correctness proof system for GC.- 1 Termination and Well-Foundedness.- 1.0 Overview.- 1.1 Termination Proofs for Deterministic Programs.- 1.2 Termination Proofs for Nondeterministic Programs.- 2 The Method of Helpful Directions.- 2.0 Introduction to Fair Termination.- 2.1 Ordinal Directed Choice of Helpful Directions.- 2.1.1 A proof rule for unconditionally-fair termination.- 2.1.2 Weakly-fair termination.- 2.1.3 Strongly-fair termination.- 2.2 State Directed Choice of Helpful Directions.- 2.2.1 Unconditionally-fair termination.- 2.2.2 Weakly-fair and strongly-fair termination.- 2.3 Inter-reducibility of the Two Methods.- 2.4 Relativized Fair Termination.- 3 The Method of Explicit Scheduler.- 3.0 Overview.- 3.0.1 Random assignments.- 3.1 Unconditionally-Fair Termination.- 3.2 Weak and Strong Fairness: n Guards.- 3.2.1 Examples for strong fairness.- 3.2.2 Alternative transformations.- 3.3 All-Levels Fairness.- 3.4 Comparing Explicit Scheduler with Helpful Directions.- 3.5 More on Fairness and Random Assignments.- 4 Extension and Generalizations of Fairness.- 4.0 Overview.- 4.1 Equifairness.- 4.1.1 Unconditional equifairness.- 4.1.2 Strong equifairness.- 4.2 Generalized Fairness.- 4.3 Extreme Fairness.- 4.3.0 Overview.- 4.3.1 Proof rules for extremely-fair termination.- 4.4 An Analysis of Predicate-Reachability Fairness.- 5 Fair Termination of Concurrent Processes.- 5.1 Overview.- 5.2 Fairness and Communicating Processes.- 5.2.1 The CSP sublanguage for communicating processes.- 5.2.2 Serialized semantics and overlapping semantics.- 5.2.3 Relativized fair termination in the serialized semantics.- 5.2.4 Proofs for the overlapping semantics.- 5.3 Fairness in Shared-Variables Concurrency.- 5.3.0 Overview.- 5.3.1 The shared-variables language SVL.- 5.3.2 Explicit scheduling of shared-variables concurrent programs.- 5.3.2.1 Unconditional fairness for synchronization-free programs.- 5.3.2.2 Explicit scheduling for weak and strong fairness in shared-variables programs.- 5.3.2.3 Proving fair termination of shared-variables programs.- 6 Syntactic Expressibility.- 6.0 Overview.- 6.1 Fixedpoints of Monotone Transformations.- 6.2 The Assertion Language L?.- 6.3 The Weakest Precondition for Fair Termination.- 6.4 Syntactic Completeness of the SFT Rule.- 6.5 The Ordinal Size for Fair-Termination Proofs.- 7 Fairness in Temporal Logic.- 7.0 Overview.- 7.1 Linear-Time Temporal-Logic (LTL).- 7.1.1 The temporal semantics of programs.- 7.1.1.1 Shared variables.- 7.1.1.2 Message passing.- 7.2 Branching-Time Temporal-Logics (BTL).- 7.2.0 Overview.- 8 The Functional Approach.- 8.0 Overview.- 8.1 CCS.- 8.2 Fairness and CCS.- 8.3 Weak and Strong Fairness in CCS.- 8.3.1 Weakly fair CCS.- 8.3.2 Strongly fair CCS.- 8.4 A Metric Characterization of CCS Fairness.- 8.4.1 Overview.- 8.4.2 The basic tools.- 8.4.3 A metric characterization of D and D?.- 8.5 Finite Delay Operators.- References.- List of Proof Rules.- Author Index.

The main purpose of this book is to bring together much of the research conducted in recent years in a subject I find both fascinating and impor­ tant, namely fairness. Much of the reported research is still in the form of technical reports, theses and conference papers, and only a small part has already appeared in the formal scientific journal literature. Fairness is one of those concepts that can intuitively be explained very brieft.y, but bear a lot of consequences, both in theory and the practicality of programming languages. Scientists have traditionally been attracted to studying such concepts. However, a rigorous study of the concept needs a lot of detailed development, evoking much machinery of both mathemat­ ics and computer science. I am fully aware of the fact that this field of research still lacks matu­ rity, as does the whole subject of theoretical studies of concurrency and nondeterminism. One symptom of this lack of maturity is the proliferation of models used by the research community to discuss these issues, a variety lacking the invariance property present, for example, in universal formalisms for sequential computing.