On Probabilistic Automata in Continuous Time

Eisentraut, Christian; Hermanns, Holger; Zhang, Lijun

doi:10.1109/lics.2010.41

Cited by 131 publications

(251 citation statements)

References 31 publications

(39 reference statements)

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“…The tool and case studies are publicly available at http://moves.rwth-aachen.de/imca. Future work will focus on the generalization of the presented algorithms to Markov automata [16], and experimentation with symbolic data structures such as multi-terminal BDDs by, e.g. exploiting Prism for the MDP analysis.…”

Section: Discussionmentioning

confidence: 99%

Quantitative Timed Analysis of Interactive Markov Chains

Guck

Han

Katoen

et al. 2012

Lecture Notes in Computer Science

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Abstract. This paper presents new algorithms and accompanying tool support for analyzing interactive Markov chains (IMCs), a stochastic timed 1 1 2 -player game in which delays are exponentially distributed. IMCs are compositional and act as semantic model for engineering formalisms such as AADL and dynamic fault trees. We provide algorithms for determining the extremal expected time of reaching a set of states, and the long-run average of time spent in a set of states. The prototypical tool Imca supports these algorithms as well as the synthesis of ε-optimal piecewise constant timed policies for timed reachability objectives. Two case studies show the feasibility and scalability of the algorithms.

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Section: Discussionmentioning

confidence: 99%

Quantitative Timed Analysis of Interactive Markov Chains

Guck

Han

Katoen

et al. 2012

Lecture Notes in Computer Science

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“…The Ipc and the Imc models have very close conceptual roots, and one can view an Ipc as a clock-ticked version of an Imc and, vice versa, one can view an Imc as the continuous time limit of an Ipc, with clock intervals tending to zero. A recent proposal [22] introduces a model that integrates both worlds in one, and develops the basic compositional theory, along the lines of Imc for this model. It is interesting to see how the available tool support can be extended to this setting.…”

Section: Discussionmentioning

confidence: 99%

Ten Years of Performance Evaluation for Concurrent Systems Using CADP

Coste

Garavel

Hermanns

et al. 2010

Lecture Notes in Computer Science

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Abstract. This article comprehensively surveys the work accomplished during the past decade on an approach to analyze concurrent systems qualitatively and quantitatively, by combining functional verification and performance evaluation. This approach lays its foundations on semantic models, such as Imc (Interactive Markov Chain) and Ipc (Interactive Probabilistic Chain), at the crossroads of concurrency theory and mathematical statistics. To support the approach, a number of software tools have been devised and integrated within the Cadp (Construction and Analysis of Distributed Processes) toolbox. These tools provide various functionalities, ranging from state space generation (Caesar and Exp.Open), state space minimization (Bcg Min and Determinator), numerical analysis (Bcg Steady and Bcg Transient), to simulation (Cunctator). Several applications of increasing complexity have been successfully handled using these tools, namely the Hubble telescope lifetime prediction, performance comparison of mutual exclusion protocols, the Scsi-2 bus arbitration protocol, the Send/Receive and Barrier primitives of Mpi (Message Passing Interface) implemented on a cache-coherent multiprocessor architecture, and the xSTream multiprocessor data-flow architecture for embedded multimedia streaming applications.

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“…An appropriate version of bisimulation equivalence is shown to be compositional, in the sense of our Theorem 3.4: it is preserved by the operators of a process calculus interpreted as IMCs. Recently a combination of probabilistic automata and IMCs has been studied in [16,10], where again compositional theories based on weak bisimulation are proposed. Here there is some sense in which at least the time-delay actions have weights associated with them; nevertheless the intuition governing them, Markovian distributions, is entirely divorced from the notion of cost or benefit as we have used in the current paper.…”

Section: Y Deng M Hennessy / Science Of Computer Programming ( ) -mentioning

confidence: 99%

Compositional reasoning for weighted Markov decision processes

Deng

Hennessy

2013

Science of Computer Programming

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h i g h l i g h t s• We develop compositional methods for reasoning about weighted Markov decision processes (MDPs).• A coinductive simulation-based behavioural preorder is proposed for weighted MDPs.• The preorder is preserved by structural operators for constructing weighted MDPs from components.• For finitary convergent processes, the preorder can be characterised by a probabilistic logic and a novel form of testing. a r t i c l e i n f o b s t r a c tWeighted Markov decision processes (MDPs) have long been used to model quantitative aspects of systems in the presence of uncertainty. However, much of the literature on such MDPs takes a monolithic approach, by modelling a system as a particular MDP; properties of the system are then inferred by analysis of that particular MDP. In contrast in this paper we develop compositional methods for reasoning about weighted MDPs, as a possible basis for compositional reasoning about their quantitative behaviour. In particular we approach these systems from a process algebraic point of view. For these we define a coinductive simulation-based behavioural preorder which is compositional in the sense that it is preserved by structural operators for constructing weighted MDPs from components.For finitary convergent processes, which are finite-state and finitely branching systems without divergence, we provide two characterisations of the behavioural preorder. The first uses a novel quantitative probabilistic logic, while the second is in terms of a novel form of testing, in which benefits are accrued during the execution of tests.

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On Probabilistic Automata in Continuous Time

Cited by 131 publications

References 31 publications

Quantitative Timed Analysis of Interactive Markov Chains

Quantitative Timed Analysis of Interactive Markov Chains

Ten Years of Performance Evaluation for Concurrent Systems Using CADP

Compositional reasoning for weighted Markov decision processes

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