Quantitative Model Checking Revisited: Neither Decidable Nor Approximable

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Quantitative model checking computes the probability values of a given property quantifying over all possible schedulers. It turns out that maximum and minimum probabilities calculated in such a way are overestimations on models of distributed systems in which components are loosely coupled and share little information with each other (and hence arbitrary schedulers may result too powerful). Therefore, we focus on the quantitative model checking problem restricted to distributed schedulers that are obtained only as a combination of local schedulers (i.e. the schedulers of each component) and show that this problem is undecidable. In fact, we show that there is no algorithm that can compute an approximation to the maximum probability of reaching a state within a given bound when restricted to distributed schedulers.

Supported by the CONICET/CNRS Cooperation project “Métodos para la Verificación de Programas Concurrentes con aspectos Aleatorios y Temporizados”, ANPCyT project PICT 26135 and CONICET project PIP 6391. The first author was partially supported by the LSIS, UMR CNRS 6168, France.