TY - GEN
T1 - On omega-languages defined by mean-payoff conditions
AU - Alur, Rajeev
AU - Degorre, Aldric
AU - Maler, Oded
AU - Weiss, Gera
PY - 2009/11/9
Y1 - 2009/11/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=70350228128&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-00596-1_24
DO - 10.1007/978-3-642-00596-1_24
M3 - Conference contribution
AN - SCOPUS:70350228128
SN - 3642005950
SN - 9783642005954
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 333
EP - 347
BT - Foundations 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.
T2 - 12th 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
Y2 - 22 March 2009 through 29 March 2009
ER -