Synthesis for PCTL in parametric Markov decision processes
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Model repair for probabilistic systems
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
PARAM: a model checker for parametric markov models
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
PRINSYS: on a quest for probabilistic loop invariants
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
Compositional probabilistic verification through multi-objective model checking
Information and Computation
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Given a parametric Markov model, we consider the problem of computing the rational function expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression is computed. Afterwards, this expression is evaluated to a closed form function representing the reachability probability. This paper investigates how this idea can be turned into an effective procedure. It turns out that the bottleneck lies in the growth of the regular expression relative to the number of states (n Θ(log n)). We therefore proceed differently, by tightly intertwining the regular expression computation with its evaluation. This allows us to arrive at an effective method that avoids this blow up in most practical cases. We give a detailed account of the approach, also extending to parametric models with rewards and with non-determinism. Experimental evidence is provided, illustrating that our implementation provides meaningful insights on non-trivial models.