Zhang, Lijun and Jansen, David N. and Nielson, Flemming and Hermanns, Holger - Efficient CSL Model Checking Using Stratification

lmcs:1085 - Logical Methods in Computer Science, July 31, 2012, Volume 8, Issue 2
Efficient CSL Model Checking Using Stratification

Authors: Zhang, Lijun and Jansen, David N. and Nielson, Flemming and Hermanns, Holger

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.


Source : oai:arXiv.org:1104.4983
DOI : 10.2168/LMCS-8(2:17)2012
Volume: Volume 8, Issue 2
Published on: July 31, 2012
Submitted on: June 16, 2011
Keywords: Computer Science - Logic in Computer Science,G.3, F.4.1, F.3.1


Share

Consultation statistics

This page has been seen 83 times.
This article's PDF has been downloaded 66 times.