Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Quantitative Analysis and Model Checking
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Quantitative solution of omega-regular games
Journal of Computer and System Sciences - STOC 2001
Stochastic Games with Branching-Time Winning Objectives
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Results on the quantitative μ-calculus qMμ
ACM Transactions on Computational Logic (TOCL)
Qualitative Determinacy and Decidability of Stochastic Games with Signals
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
Model Checking Games for the Quantitative μ-Calculus
Theory of Computing Systems - Special Title: Symposium on Theoretical Aspects of Computer Science; Guest Editors: Susanne Albers, Pascal Weil
Characterising probabilistic processes logically
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
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The probabilistic modal µ-calculus pLµ (often called the quantitative µ-calculus) is a generalization of the standard modal µ-calculus designed for expressing properties of probabilistic labeled transition systems. The syntax of pLµ formulas coincides with that of the standard modal µ-calculus. Two equivalent semantics have been studied for pLµ, both assigning to each process-state p a value in [0, 1] representing the probability that the property expressed by the formula will hold in p: a denotational semantics and a game semantics given by means of two player stochastic games. In this paper we extend the logic pLµ with a second conjunction called product, whose semantics interprets the two conjuncts as probabilistically independent events. This extension allows one to encode useful operators, such as the modalities with probability one and with non-zero probability. We provide two semantics for this extended logic: one denotational and one based on a new class of games which we call tree games. The main result is the equivalence of the two semantics. The proof is carried out in ZFC set theory extended with Martin's Axiom at the first uncountable cardinal.