Efficient CSL Model Checking Using Stratification

TL;DR

This paper introduces an efficient polynomial-time approximation algorithm for full CSL model checking on continuous-time Markov chains by transforming them into stratified CTMCs, enabling scalable and decidable verification.

Contribution

It presents a novel measure-preserving transformation to convert any CTMC into a stratified form, facilitating efficient CSL model checking and ensuring decidability for general CTMCs.

Findings

Polynomial-time approximation for full CSL model checking.

Transformation preserves measure and is linear in time and space.

Ensures decidability for general CTMCs.

Abstract

For continuous-time Markov chains, the model-checking problem with respect to continuous-time stochastic logic (CSL) has been introduced and shown to be decidable by Aziz, Sanwal, Singhal and Brayton in 1996. Their proof can be turned into an approximation algorithm with worse than exponential complexity. In 2000, Baier, Haverkort, Hermanns and Katoen presented an efficient polynomial-time approximation algorithm for the sublogic in which only binary until is allowed. In this paper, we propose such an efficient polynomial-time approximation algorithm for full CSL. The key to our method is the notion of stratified CTMCs with respect to the CSL property to be checked. On a stratified CTMC, the probability to satisfy a CSL path formula can be approximated by a transient analysis in polynomial time (using uniformization). We present a measure-preserving, linear-time and -space transformation of any CTMC into an equivalent, stratified one. This makes the present work the centerpiece of a broadly applicable full CSL model checker. Recently, the decision algorithm by Aziz et al. was shown to work only for stratified CTMCs. As an additional contribution, our measure-preserving transformation can be used to ensure the decidability for general CTMCs.