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Lecture Notes in Computer Science: Foundations of Software Science and Computational Structures
In quantitative verification, system states/transitions have associated payoffs, and these are used to associate mean-payoffs with infinite behaviors. In this paper, we propose to define ω-languages via Boolean queries over mean-payoffs. Requirements concerning averages such as “the number of messages lost is negligible” are not ω-regular, but specifiable in our framework. We show that, for closure under intersection, one needs to consider multi-dimensional payoffs. We argue that the acceptance condition needs to examine the set of accumulation points of sequences of mean-payoffs of prefixes, and give a precise characterization of such sets. We propose the class of multi-threshold mean-payoff languages using acceptance conditions that are Boolean combinations of inequalities comparing the minimal or maximal accumulation point along some coordinate with a constant threshold. For this class of languages, we study expressiveness, closure properties, analyzability, and Borel complexity.
The original publication is available at www.springerlink.com
Rajeev Alur, Aldric Degorre, Oded Maler, and Gera Weiss, "On Omega-Languages Defined by Mean-Payoff Conditions", Lecture Notes in Computer Science: Foundations of Software Science and Computational Structures 5504, 333-347. March 2009. http://dx.doi.org/10.1007/978-3-642-00596-1_24
Date Posted: 17 July 2012