Numerical vs. statistical probabilistic model checking

Abstract

Abstract. Numerical analysis based on uniformisation and statistical techniques based on sampling and simulation are two distinct approaches for transient analysis of stochastic systems. We compare the two solution techniques when applied to the verification of time-bounded until formulae in the temporal stochastic logic CSL. This study differs from most previous comparisons of numerical and statistical approaches in that CSL model checking is a hypothesis testing problem rather than a parameter estimation problem. We can therefore rely on highly efficient sequential acceptance sampling tests, which enables statistical solution techniques to quickly return a result with some uncertainty. This suggests that statistical techniques can be useful as a first resort during system prototyping, rather than as a last resort as often suggested. We also propose a novel combination of the two solution techniques for verifying CSL queries with nested probabilistic operators.

Stochastic Model Checking

“…Related topic include: probabilistic generalisations of bisimulation and simulation relations for DTMCs [49,57] and for CTMCs [17,11]; and approximate methods for stochastic model checking based on discrete event simulation [33,63]. Stochastic model checkers SMART [19], E T MC 2 [34] and MRMC [39] have similarities with the PRISM model checker described here.…”

Simulation and Analysis of Distributed Systems in Klaim

“…To overcome the state explosion problem, a statistical model-checker has been also implemented in SAM. The statistical approach has been successfully used in existing model checkers [15,21,24,25].…”

A Probabilistic Formal Analysis Approach to Cross Layer Optimization in Distributed Embedded Systems

“…Here, black-box means that the system cannot be controlled to generate execution traces, or trajectories, on demand starting from arbitrary states. The implementation of sequential testing and black-box testing can be found as part of the Ymer [15,16] and VeStA [14] tools, respectively. -Statistical Quantitative Analysis: Statistical evaluation can be performed with a large quantity of data that follows a normal distribution, and hence allows the estimation of the expected value and our confidence.…”

“…Ymer [15,16] implements statistical techniques, based on discrete event simulation and sequential acceptance sampling for CSL model checking. The system is modeled by continuous-time Markov chains (CTMCs) and generalized semiMarkov processes (GSMPs).…”