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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.

Keywords

Convex Hull Accumulation Point Linear Temporal Logic Closure Property Acceptance Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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