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Parametric Markov Chains: PCTL Complexity and Fraction-free Gaussian Elimination by Hutschenreiter, Lisa; Baier, Christel; Klein, Joachim is a scholarly article available to read on EtoBox.

What is Parametric Markov Chains: PCTL Complexity and Fraction-free Gaussian Elimination about?

Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for the parameters. Among the tasks typically addressed in the analysis of parametric Markov chains are (1) the computation of closed-form solutions for reachabilty probabilities and other quantitative measures and (2) finding symbolic representations of the set of parameter valuations for which a given temporal logical formula holds as well as (3) the decision variant of (2) that asks whether there exists a parameter valuation where a temporal logical formula holds. Our contribution to (1) is to show that existing implementations for computing rational functions for reachability probabilities or expected costs in parametric Markov chains can be improved by using fraction-free Gaussian elimination, a long-known technique for linear equation systems with parametric coefficients. Our contribution to (2) and (3) is a complexity-theoretic discussion of the model checking problem for parametric Markov chains and probabilistic computation tree logic (PCTL)

Author

Hutschenreiter, Lisa; Baier, Christel; Klein, Joachim

Published

2017

Language

EN