4,495 research outputs found
Probabilistic Bisimulations for PCTL Model Checking of Interval MDPs
Verification of PCTL properties of MDPs with convex uncertainties has been
investigated recently by Puggelli et al. However, model checking algorithms
typically suffer from state space explosion. In this paper, we address
probabilistic bisimulation to reduce the size of such an MDPs while preserving
PCTL properties it satisfies. We discuss different interpretations of
uncertainty in the models which are studied in the literature and that result
in two different definitions of bisimulations. We give algorithms to compute
the quotients of these bisimulations in time polynomial in the size of the
model and exponential in the uncertain branching. Finally, we show by a case
study that large models in practice can have small branching and that a
substantial state space reduction can be achieved by our approach.Comment: In Proceedings SynCoP 2014, arXiv:1403.784
Transient Reward Approximation for Continuous-Time Markov Chains
We are interested in the analysis of very large continuous-time Markov chains
(CTMCs) with many distinct rates. Such models arise naturally in the context of
reliability analysis, e.g., of computer network performability analysis, of
power grids, of computer virus vulnerability, and in the study of crowd
dynamics. We use abstraction techniques together with novel algorithms for the
computation of bounds on the expected final and accumulated rewards in
continuous-time Markov decision processes (CTMDPs). These ingredients are
combined in a partly symbolic and partly explicit (symblicit) analysis
approach. In particular, we circumvent the use of multi-terminal decision
diagrams, because the latter do not work well if facing a large number of
different rates. We demonstrate the practical applicability and efficiency of
the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit
Multi-objective Robust Strategy Synthesis for Interval Markov Decision Processes
Interval Markov decision processes (IMDPs) generalise classical MDPs by
having interval-valued transition probabilities. They provide a powerful
modelling tool for probabilistic systems with an additional variation or
uncertainty that prevents the knowledge of the exact transition probabilities.
In this paper, we consider the problem of multi-objective robust strategy
synthesis for interval MDPs, where the aim is to find a robust strategy that
guarantees the satisfaction of multiple properties at the same time in face of
the transition probability uncertainty. We first show that this problem is
PSPACE-hard. Then, we provide a value iteration-based decision algorithm to
approximate the Pareto set of achievable points. We finally demonstrate the
practical effectiveness of our proposed approaches by applying them on several
case studies using a prototypical tool.Comment: This article is a full version of a paper accepted to the Conference
on Quantitative Evaluation of SysTems (QEST) 201
Efficient CSL Model Checking Using Stratification
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.Comment: 18 pages, preprint for LMCS. An extended abstract appeared in ICALP
201
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