Affiliation:
1. IBM Research---Zurich, Switzerland
2. PPS-CNRS and Univ Paris Diderot, France
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,
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
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
ω
-regular properties and bounded Borel measures. That is, an
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
14 articles.
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