On omega-languages defined by mean-payoff conditions

Rajeev Alur, Aldric Degorre, Oded Maler, Gera Weiss

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

25 Scopus citations

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.

Original languageEnglish
Title of host publicationFoundations of Software Science and Computational Structures - 12th International Conference, FOSSACS 2009 - Part of the Joint European Conf. on Theory and Practice of Software, ETAPS 2009, Proc.
Pages333-347
Number of pages15
DOIs
StatePublished - 9 Nov 2009
Externally publishedYes
Event12th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2009. Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009 - York, United Kingdom
Duration: 22 Mar 200929 Mar 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5504 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference12th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2009. Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Country/TerritoryUnited Kingdom
CityYork
Period22/03/0929/03/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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