Section: New Results
Quantitative systems
Real-time probabilistic systems
This year, new results were obtained in the cooperation of Stefan Haar with the DistribCom team in Rennes:
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Monotonicity : We established criteria to check whether and when global latencies depend in a monotonic way on local latencies, see [14] .
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Criticality : parallelism, branching and synchronization in asynchronous compositions may either hide or accentuate individual delays. Some components' behavior is critical for global performance while the variation in performance of other components is without effect on the composite performance. Combining the analysis of partially ordered structure and of probabilistic delays we show in [13] how to identify critical components, and thus to allocate resources efficiently in view of improving performance.
Moreover this year, Serge Haddad developped jointly an efficient (approximate) method for the quantitative model checking of PCTL formula for interval-valued discrete time Markov chains (IMC). Whilst the exact model checking has been shown to be NP and co-NP hard, our method is polynomial-time. Furthermore, this procedure returns more refined answers than traditional ones: YES, NO, DON'T KNOW. Thus we may provide useful partial information for modelers in the "DON'T KNOW" case.
Weighted Automata
New results were obtained on weighted pushdown automata, which form the basis for interprocedural dataflow analysis. The problem is related to studying fixed-point equations on idempotent semirings. The efficiency with which these problems can be solved depends on certain algebraic properties of the weights involved. In comparison with previous work, we managed to establish more general properties that still enable an efficient solution [22] .
Weighted versus Probabilistic Logics
Benedikt Bollig and Paul Gastin have introduced for arbitrary semirings weighted versions of MSO and CTL that generalize both the boolean logics and their probabilistic versions. Being able to use arbitrary semirings to specify quantitative properties of systems allows to deal with new quantities such as energy, rewards, expected rewards, etc. They established expressiveness results giving translations from weighted and probabilistic CTL into weighted MSO. This should open the way to more general quantitative verification of systems. This work was presented in the invited lecture [7] .
