2016 # Parameter Synthesis for Markov Models: Faster Than Ever

**Abstract:** Abstract. We propose a conceptually simple technique for verifying probabilistic models whose transition probabilities are parametric. The key is to replace parametric transitions by nondeterministic choices of extremal values. Analysing the resulting parameter-free model using off-theshelf means yields (refinable) lower and upper bounds on probabilities of regions in the parameter space. The technique outperforms the existing analysis of parametric Markov chains by several orders of magnitude regarding both r…

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“…Setup. In our first set of benchmarks, we adopt parametric MDPs and MCs from [32]. Essentially, the technique from that paper allows to approximate the percentage of instantiations that satisfy (or do not satisfy) a specification.…”

confidence: 99%

“…Setup. In our first set of benchmarks, we adopt parametric MDPs and MCs from [32]. Essentially, the technique from that paper allows to approximate the percentage of instantiations that satisfy (or do not satisfy) a specification.…”

confidence: 99%

“…Our approach can be easily extended to also support timeunbounded properties by using the method of [25] for parameter synthesis of discrete-time Markov models and properties expressed by time-unbounded formulae of probabilistic computation tree logic.…”

confidence: 99%

“…Fig. 2 shows the resulting model, encoded in the PRISM modelling language extended with the evolve constructs from Section IV-C. As in [31], we model separately the software and hardware failures and repairs, for both the master server (lines [22][23][24][25] and the chunk servers (lines [26][27][28][29][30][31], and assume that loss of chunk copies due to chunk server failures leads to further chunk replications, which is an order of magnitude slower if c = 0 and a backup of the chunk must be used (line 32).…”

confidence: 99%

“…Despite the significant progress in the last years in analysing pMCs [10,15,41], the scalability of algorithms severely lacks behind methods for ordinary MCs.…”

confidence: 99%