On Omega-Languages Defined by Mean-Payoff Conditions

  • Rajeev Alur
  • Aldric Degorre
  • Oded Maler
  • Gera Weiss
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5504)

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Rajeev Alur
    • 1
  • Aldric Degorre
    • 2
  • Oded Maler
    • 2
  • Gera Weiss
    • 1
  1. 1.Dept. of Computer and Information ScienceUniversity of PennsylvaniaUSA
  2. 2.CNRS - Verimag, University of GrenobleFrance

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