Nested Reachability Approximation for Discrete-Time Markov Chains with Univariate Parameters

Guoxin Su, David S. Rosenblum

Abstract: As models of real-world stochastic systems usually contain inaccurate information, probabilistic model checking for models with open or undetermined parameters has recently aroused research attention. In this paper, we study a kind of parametric variant of Discrete-time Markov Chains with uncertain transition probabilities, namely Parametric Markov Chains (PMCs), and probabilistic reachability properties with nested PCTL probabilistic operators. Such properties for a PMC with a univariate parameter define univariate real functions, called reachability functions, that map the parameter to reachability probabilities. An interesting application of these functions is sensitivity and robustness analysis of probabilistic model checking. However, a pitfall of computing the closed-form expression of a reachability function is the possible dynamism of its constraint set and target set. We pursue interval approximations for reachability functions with high accuracy. In particular, for reachability functions involving only single-nested probabilistic operators, we provide an efficient algorithm to compute their approximations. We demonstrate the applicability of our approach with a case study on a NAND multiplexing unit.

External IDs:dblp:conf/atva/SuR14