5,516 research outputs found
Model Checking Markov Chains with Actions and State Labels
In the past, logics of several kinds have been proposed for reasoning about discrete- or continuous-time Markov chains. Most of these logics rely on either state labels (atomic propositions) or on transition labels (actions). However, in several applications it is useful to reason about both state-properties and action-sequences. For this purpose, we introduce the logic asCSL which provides powerful means to characterize execution paths of Markov chains with actions and state labels. asCSL can be regarded as an extension of the purely state-based logic asCSL (continuous stochastic logic). \ud
In asCSL, path properties are characterized by regular expressions over actions and state-formulas. Thus, the truth value of path-formulas does not only depend on the available actions in a given time interval, but also on the validity of certain state formulas in intermediate states.\ud
We compare the expressive power of CSL and asCSL and show that even the state-based fragment of asCSL is strictly more expressive than CSL if time intervals starting at zero are employed. Using an automaton-based technique, an asCSL formula and a Markov chain with actions and state labels are combined into a product Markov chain. For time intervals starting at zero we establish a reduction of the model checking problem for asCSL to CSL model checking on this product Markov chain. The usefulness of our approach is illustrated by through an elaborate model of a scalable cellular communication system for which several properties are formalized by means of asCSL-formulas, and checked using the new procedure
A Markov Chain Model Checker
Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen Twente Markov Chain Checker ), where properties are expressed in appropriate extensions of CTL. We illustrate the general bene ts of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of )
A tool for model-checking Markov chains
Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker EĂMC2, where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of EĂMC2
A uniformization-based algorithm for model checking the CSL until operator on labeled queueing networks
We present a model checking procedure for the CSL until operator on the CTMCs that underlie Jackson queueing networks. The key issue lies in the fact that the underlying CTMC is infinite in as many dimension as there are queues in the JQN. We need to compute the transient state probabilities for all goal states and for all possible starting states. However, for these transient probabilities no computational procedures are readily available. The contribution of this paper is the proposal of a new uniformization-based approach to compute the transient state probabilities. Furthermore, we show how the highly structured state space of JQNs allows us to compute the possible infinite satisfaction set for until formulas. A case study on an e-business site shows the feasibility of our approach
Beyond Model-Checking CSL for QBDs: Resets, Batches and Rewards
We propose and discuss a number of extensions to quasi-birth-death models (QBDs) for which CSL model checking is still possible, thus extending our recent work on CSL model checking of QBDs. We then equip the QBDs with rewards, and discuss algorithms and open research issues for model checking CSRL for QBDs with rewards
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
When are Stochastic Transition Systems Tameable?
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of
decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness
allows one to lift most good properties from finite Markov chains to
denumerable ones, and therefore to adapt existing verification algorithms to
infinite-state models. Decisive Markov chains however do not encompass
stochastic real-time systems, and general stochastic transition systems (STSs
for short) are needed. In this article, we provide a framework to perform both
the qualitative and the quantitative analysis of STSs. First, we define various
notions of decisiveness (inherited from [1]), notions of fairness and of
attractors for STSs, and make explicit the relationships between them. Then, we
define a notion of abstraction, together with natural concepts of soundness and
completeness, and we give general transfer properties, which will be central to
several verification algorithms on STSs. We further design a generic
construction which will be useful for the analysis of {\omega}-regular
properties, when a finite attractor exists, either in the system (if it is
denumerable), or in a sound denumerable abstraction of the system. We next
provide algorithms for qualitative model-checking, and generic approximation
procedures for quantitative model-checking. Finally, we instantiate our
framework with stochastic timed automata (STA), generalized semi-Markov
processes (GSMPs) and stochastic time Petri nets (STPNs), three models
combining dense-time and probabilities. This allows us to derive decidability
and approximability results for the verification of these models. Some of these
results were known from the literature, but our generic approach permits to
view them in a unified framework, and to obtain them with less effort. We also
derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page
On the connections between PCTL and Dynamic Programming
Probabilistic Computation Tree Logic (PCTL) is a well-known modal logic which
has become a standard for expressing temporal properties of finite-state Markov
chains in the context of automated model checking. In this paper, we give a
definition of PCTL for noncountable-space Markov chains, and we show that there
is a substantial affinity between certain of its operators and problems of
Dynamic Programming. After proving some uniqueness properties of the solutions
to the latter, we conclude the paper with two examples to show that some
recovery strategies in practical applications, which are naturally stated as
reach-avoid problems, can be actually viewed as particular cases of PCTL
formulas.Comment: Submitte
MeGARA: Menu-based Game Abstraction and Abstraction Refinement of Markov Automata
Markov automata combine continuous time, probabilistic transitions, and
nondeterminism in a single model. They represent an important and powerful way
to model a wide range of complex real-life systems. However, such models tend
to be large and difficult to handle, making abstraction and abstraction
refinement necessary. In this paper we present an abstraction and abstraction
refinement technique for Markov automata, based on the game-based and
menu-based abstraction of probabilistic automata. First experiments show that a
significant reduction in size is possible using abstraction.Comment: In Proceedings QAPL 2014, arXiv:1406.156
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