Departmental Papers (CIS)

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Conference Paper

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Alur, R., Degorre, A., Maler, O., & Weiss, G., On Omega-Languages Defined by Mean-Payoff Conditions, 12th International Conference on Foundations of Software Science and Computation Structures, March 2009, doi: 10.1007/978-3-642-00596-1_24


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.



Date Posted: 17 July 2012