Three-valued abstraction for probabilistic systems

Katoen, Joost-Pieter; Klink, Daniel; Leucker, Martin; Wolf, Verena

doi:10.1016/j.jlap.2012.03.007

Cited by 36 publications

(24 citation statements)

References 14 publications

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“…Let Now consider the set Q of all matrices with row sums equal 0 between Q À 0:1E and Q þ 0:1E where E is the matrix of ones. Clearly, Q is a convex set of matrices and let Q and Q be the corresponding upper and lower envelope operators as defined in (11) and (12) respectively. We consider the equations d dt f t ¼ Qf t and d dt f t ¼ Qf t respectively on the interval ½0; 2 with the initial solution f I ¼ ½1; 0; 0:5; À0:2 T .…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Another field where Markov chains with multiple transition scenarios are studied are Markov decision processes [1,2,11], where transition rate scenario is selected from a set of scenarios using so-called schedulers, which depend on the process history and rule the transition rates until the next change of state occurs. The main difference between our model and Markov decision process, apart from some technical differences in presentation of the sets of transition scenarios, is that in our model transition rate scenarios depend purely on time and may change during the time before a transition occurs.…”

Section: Introductionmentioning

confidence: 99%

“…At any time, the only assumption on the transition rates is that they belong to the prescribed set. In this sense our model is very general in comparison with the related models where either continuity or differentiability [9] are required, or that the transition rates only change when transition occurs [1,2,11]. The modelling approach with lower and upper expectation functionals and transition operators, allows us to translate the problem to the form of non-linear matrix differential equations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient computation of the bounds of continuous time imprecise Markov chains

Škulj¹

2015

Applied Mathematics and Computation

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Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient computation of the bounds of continuous time imprecise Markov chains

Škulj¹

2015

Applied Mathematics and Computation

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“…IDTMCs were introduced in [14,16] to allow a realistic encoding of stochastic systems. More recently, IDTMC (called Abstract DTMC) were used for model checking of DTMCs for abstraction purposes to overcome the state space explosion problem [6,15].…”

Section: Introductionmentioning

confidence: 99%

Efficient Probabilistic Model Checking of Systems with Ranged Probabilities

Ghorbal

Duggirala

Kahlon

et al. 2012

Lecture Notes in Computer Science

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Abstract. We introduce a new technique to model check reachability properties on Interval Discrete-Time Markov Chains (IDTMC). We compute a sound overapproximation of the probabilities of satisfying a given property where the accuracy is characterized in terms of error bounds. We leverage affine arithmetic to propagate the first-order error terms. Higher-order error terms are bounded using interval arithmetic.

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“…We present the theoretical foundations of aggressive abstraction of Markov models [6] and show how this technique can be applied in a compositional way. This enables the component-wise abstraction of large models [7,11].…”

mentioning

confidence: 99%

Software Engineering and Formal Methods

2014

Lecture Notes in Computer Science

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Probabilistic model checking -the verification of models incorporating random phenomena -has enjoyed a rapid increase of interest. Thanks to the availability of mature tool support and efficient verification algorithms, probabilistic model checking has been successfully applied to case studies from various areas, such as randomized (distributed) algorithms, planning and AI, security, hardware, stochastic scheduling, reliability analysis, and systems biology [9]. In addition, model-checking techniques have been adopted by mainstream model-based performance and dependability tools as effective analysis means. Probabilistic model checking can thus be viewed as a viable alternative and extension to traditional model-based performance analysis [1].Typical properties that are checked are quantitative reachability objectives, such as: does the probability to reach a certain set of goal states (by avoiding illegal states) exceed 1 2 ? Extra constraints can be incorporated as well that e.g., require the goal to be reached within a certain number of transitions, within a certain budget, or within a real-time deadline. For models exhibiting both transition probabilities and non-determinism, maximal and minimal probabilities are considered. Intricate combinations of numerical (or simulation) techniques for Markov chains, optimization algorithms, and traditional CTL or LTL modelchecking algorithms result in simple, yet very efficient verification procedures [2,10]. Verifying time-bounded reachability properties on continuous-time models of tens of millions of states usually is a matter of seconds. Using symbolic representation techniques such as multi-terminal BDDs, much larger systems can be treated efficiently as well. A gentle introduction can be found in [5].Like in the traditional setting, probabilistic model checking suffers from the curse of dimensionality: the number of states grows exponentially in the number of system components and cardinality of data domains. This hampers the analysis of real-life systems such as biological models involving thousands of molecules [12], and software models of on-board aerospace systems that incorporate probabilistic error models of various system components on top of the "nominal" system behaviour [3].This talk considers the theory and practice of aggressive abstraction of discrete-time and continuous-time Markov models. Our abstraction technique is based on a partitioning of the concrete state space that is typically much coarser than e.g., bisimulation minimisation. We exploit three-valued abstraction [4] in which a temporal logic formula evaluates to either true, false, or indefinite. In this setting, abstraction is conservative for both positive and negative verification results; in our setting this means that the analysis yields bounds on the desired probability measures. If the verification of the abstract model yields an indefi-

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Three-valued abstraction for probabilistic systems

Cited by 36 publications

References 14 publications

Efficient computation of the bounds of continuous time imprecise Markov chains

Efficient computation of the bounds of continuous time imprecise Markov chains

Efficient Probabilistic Model Checking of Systems with Ranged Probabilities

Software Engineering and Formal Methods

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