### Defining Fairness in Reactive and Concurrent SystemsDefining Fairness in Reactive and Concurrent Systems

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 Author Vlzer, Hagen ♦ Varacca, Daniele Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2012 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Fairness ♦ Concurrent systems ♦ Game theory ♦ Machine closure ♦ Model checking ♦ Temporal logic ♦ Temporal properties ♦ Topology Abstract We define when a linear-time temporal property is a fairness property with respect to a given system. This captures the essence shared by most fairness assumptions that are used in the specification and verification of reactive and concurrent systems, such as weak fairness, strong fairness, $\textit{k}-fairness,$ and many others. We provide three characterizations of fairness: a language-theoretic, a game-theoretic, and a topological characterization. It turns out that the fairness properties are the sets that are “large” from a topological point of view, that is, they are the $\textit{co-meager}$ sets in the natural topology of runs of a given system. This insight provides a link to probability theory where a set is “large” when it has measure 1. While these two notions of largeness are similar, they do not coincide in general. However, we show that they coincide for $\textit{ω}-regular$ properties and bounded Borel measures. That is, an $\textit{ω}-regular$ temporal property of a finite-state system has measure 1 under a bounded Borel measure if and only if it is a fairness property with respect to that system. The definition of fairness leads to a generic relaxation of correctness of a system in linear-time semantics. We define a system to be fairly correct if there exists a fairness assumption under which it satisfies its specification. Equivalently, a system is fairly correct if the set of runs satisfying the specification is topologically large. We motivate this notion of correctness and show how it can be verified in a system. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2012-06-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 59 Issue Number 3 Page Count 37 Starting Page 1 Ending Page 37

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Source: ACM Digital Library