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45
Modelchecking algorithms for continuoustime Markov chains
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2003
"... Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realt ..."
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Cited by 128 (26 self)
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Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realtime probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al., contains a timebounded until operator to express probabilistic timing properties over paths as well as an operator to express steadystate probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steadystate operator) and a Volterra integral equation system (for timebounded until). We then show that the problem of modelchecking timebounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a wellknown notion for aggregating CTMCs, preserves the validity of all formulas in the logic.
Model checking continuoustime Markov chains by transient analysis
, 2000
"... . The verification of continuoustime Markov chains (CTMCs) against continuous stochastic logic (CSL) [3, 6], a stochastic branchingtime temporal logic, is considered. CSL facilitates among others the specification of steadystate properties and the specification of probabilistic timing properties o ..."
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Cited by 69 (17 self)
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. The verification of continuoustime Markov chains (CTMCs) against continuous stochastic logic (CSL) [3, 6], a stochastic branchingtime temporal logic, is considered. CSL facilitates among others the specification of steadystate properties and the specification of probabilistic timing properties of the form P# #p(#1 U I #2 ), for state formulas #1 and #2 , comparison operator ##, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using e#cient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a wellknown notion for aggregating CTMCs, preserves the validity of all CSLformulas. In 12th Annual Symposium on Computer Aided Verification, CAV 2000, c # SpringerVerlag 2000 Chicago,...
A Markov Chain Model Checker
, 2000
"... . 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]. ..."
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Cited by 45 (19 self)
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. 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 continuoustime Markov chains, the ErlangenTwente Markov Chain Checker (E MC 2 ), 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 first successful applications of the tool to nontrivial examples, highlighting lessons learned during development and application of E T MC 2 . 1 Introduction Markov chains are widely used as simple yet adequate models in diverse areas, ranging from mathematics and computer science to other disciplines such as operations research, industrial engine...
On combining functional verification and performance evaluation using CADP
 FME 2002: International Symposium of Formal Methods Europe, volume 2391 of LNCS
, 2002
"... Abstract. Considering functional correctness and performance evaluation in a common framework is desirable, both for scientific and economic reasons. In this paper, we describe how the Cadp toolbox, originally designed for verifying the functional correctness of Lotos specifications, can also be use ..."
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Cited by 30 (7 self)
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Abstract. Considering functional correctness and performance evaluation in a common framework is desirable, both for scientific and economic reasons. In this paper, we describe how the Cadp toolbox, originally designed for verifying the functional correctness of Lotos specifications, can also be used for performance evaluation. We illustrate the proposed approach by the performance study of the Scsi2 bus arbitration protocol. 1
Towards Model Checking Stochastic Process Algebra
, 2000
"... . Stochastic process algebra have been proven useful because they allow behaviouroriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviouroriented style supports composition and abstraction in a natural way. However, analysis of stocha ..."
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Cited by 23 (8 self)
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. Stochastic process algebra have been proven useful because they allow behaviouroriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviouroriented style supports composition and abstraction in a natural way. However, analysis of stochastic process algebra models is stateoriented, because standard numerical analysis is typically based on the calculation of (transient and steady) state probabilities. This shift of paradigms hampers the acceptance of the process algebraic approach by performance modellers. In this paper, we develop an entirely behaviouroriented analysis technique for stochastic process algebra. The key contribution is an actionbased temporal logic to describe behavioursofinterest, together with a model checking algorithm to derive the probability with which a stochastic process algebra model exhibits a given behaviourofinterest. 1 Introduction The analysis of systems with respect to their performance...
PMaude: Rewritebased specification language for probabilistic object systems
 Electronic Notes in Theoretical Computer Science
, 2005
"... We introduce a rewritebased specification language for modelling probabilistic concurrent and distributed systems. The language, based on PMaude, has both a rigorous formal basis and the characteristics of a highlevel rulebased programming language. Furthermore, we provide tool support for perfor ..."
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Cited by 23 (5 self)
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We introduce a rewritebased specification language for modelling probabilistic concurrent and distributed systems. The language, based on PMaude, has both a rigorous formal basis and the characteristics of a highlevel rulebased programming language. Furthermore, we provide tool support for performing discreteevent simulations of models written in PMaude, and for statistically analyzing various quantitative aspects of such models based on the samples that are generated through discreteevent simulation. Because distributed and concurrent communication protocols can be modelled using actors (concurrent objects with asynchronous message passing), we provide an actor PMaude module. The module aids writing specifications in a probabilistic actor formalism. This allows us to easily write specifications that are purely probabilistic – and not just nondeterministic. The absence of such (unquantified) nondeterminism in a probabilistic system is necessary for a form of statistical analysis that we also discuss. Specifically, we introduce a query language called Quantitative Temporal Expressions (or QuaTEx in short), to query various quantitative aspects of a probabilistic model. We also describe a statistical technique to evaluate QuaTEx expressions for a probabilistic model. 1
Decision Algorithms for Probabilistic Bisimulation
, 2002
"... We propose decision algorithms for bisimulation relations de ned on probabilistic automata, a model for concurrent nondeterministic systems with randomization. The algorithms decide both strong and weak bisimulation relations based on deterministic as well as randomized schedulers. These algori ..."
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Cited by 22 (3 self)
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We propose decision algorithms for bisimulation relations de ned on probabilistic automata, a model for concurrent nondeterministic systems with randomization. The algorithms decide both strong and weak bisimulation relations based on deterministic as well as randomized schedulers. These algorithms extend and complete other known algorithms for simpler relations and models. The algorithm we present for strong probabilistic bisimulation has polynomial time complexity, while the algorithm for weak probabilistic bisimulation is exponential; however we argue that the latter is feasible in practice.
On the use of MTBDDs for performability analysis and verification of stochastic systems
"... This paper describes how to employ Multi Terminal Binary Decision Diagrams (MTBDD) for the construction and analysis of a general class of models that exhibit stochastic, probabilistic and nondeterministic behaviour. It is shown how the notorious problem of state space explosion can be circumvented ..."
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Cited by 19 (8 self)
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This paper describes how to employ Multi Terminal Binary Decision Diagrams (MTBDD) for the construction and analysis of a general class of models that exhibit stochastic, probabilistic and nondeterministic behaviour. It is shown how the notorious problem of state space explosion can be circumvented by compositionally constructing symbolic (i.e. MTBDDbased) representations of complex systems from smallscale components. We emphasise, however, that compactness of the representation can only be achieved if heuristics are applied with insight into the structure of the system under investigation. We report on our experiences concerning compact representation, performance analysis and verification of performability properties.
ModelChecking Large Structured Markov Chains
, 2002
"... This paper presents algorithms and experimental results for modelchecking continuous time Markov chains (CTMCs) based on a structured analysis approach. In this approach, a CTMC is represented as a term in Kronecker algebra that reects the component structure of the system model. Such representati ..."
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Cited by 14 (3 self)
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This paper presents algorithms and experimental results for modelchecking continuous time Markov chains (CTMCs) based on a structured analysis approach. In this approach, a CTMC is represented as a term in Kronecker algebra that reects the component structure of the system model. Such representations can be obtained in a natural way from various highlevel speci cation formalisms, such as stochastic extensions of Petri nets, process algebras or activity networks. Properties are expressed in Continuous Stochastic Logic (CSL) which includes means to express transient, steadystate and path performance measures. This paper describes novel modelchecking algorithms for CSL that fully exploit the compositional description of the CTMC. This yields an eective way to combat the statespace explosion problem and enables the modelchecking of fairly large Markov chains. Furthermore, we show how statespace aggregation (modulo bisimulation) and the elimination of vanishing states can be done in a componentwise manner. To demonstrate the applicability of the approach, and to assess the eciency of our algorithms, we analyze a stochastic Petri netmodel of a workstation cluster system and a simple queueing network.
Branching cells as local states for event structures and nets: Probabilistic applications
 In Proceedings of 8th FoSSaCS, volume 3441 of LNCS
, 2005
"... Abstract. We study the concept of choice for true concurrency models such as prime event structures and safe Petri nets. We propose a dynamic variation of the notion of cluster previously introduced for nets. This new object is defined for event structures, it is called a branching cell. Our aim is ..."
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Cited by 14 (8 self)
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Abstract. We study the concept of choice for true concurrency models such as prime event structures and safe Petri nets. We propose a dynamic variation of the notion of cluster previously introduced for nets. This new object is defined for event structures, it is called a branching cell. Our aim is to bring an interpretation of branching cells as a right notion of “local state”, for concurrent systems. We illustrate the above claim through applications to probabilistic concurrent models. In this respect, our results extends in part previous work by VaraccaVölzerWinskel on probabilistic confusion free event structures. We propose a construction for probabilities over socalled locally finite event structures that makes concurrent processes probabilistically independent—simply attach a dice to each branching cell; dices attached to concurrent branching cells are thrown independently. Furthermore, we provide a true concurrency generalization of Markov chains, called Markov nets. Unlike in existing variants of stochastic Petri nets, our approach randomizes Mazurkiewicz traces, not firing sequences. We show in this context the Law of Large Numbers (LLN), which confirms that branching cells deserve the status of local state. Our study was motivated by the stochastic modeling of fault propagation and alarm correlation in telecommunications networks and services. It provides the foundations for probabilistic diagnosis, as well as the statistical distributed learning of such models. 1