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
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 of this Version
Lecture Notes in Computer Science: Foundations of Software Science and Computational Structures
The original publication is available at www.springerlink.com
Date Posted: 17 July 2012