1,182 research outputs found

    Confluence reduction for Markov automata

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    Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models generated by such specifications. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep these models small. We define the notion of confluence directly on Markov automata, and discuss how to syntactically detect confluence on the MAPA language as well. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude

    Calculating Ï„-confluence compositionally

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    Ï„-confluence is a reduction technique used in enumerative model-checking of labeled transition systems to avoid the state explosion problem. In this paper, we propose a new on-the-fly algorithm to calculate partial Ï„-confluence, and propose new techniques to do so on large systems in a compositional manner. Using information inherent in the way a large system is composed of smaller systems, we show how we can deduce partial Ï„-confluence in a computationally cheap manner. Finally, these techniques are applied to a number of case studies, including the rel/REL atomic multicast protocol.peer-reviewe

    Confluence Detection for Transformations of Labelled Transition Systems

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    The development of complex component software systems can be made more manageable by first creating an abstract model and then incrementally adding details. Model transformation is an approach to add such details in a controlled way. In order for model transformation systems to be useful, it is crucial that they are confluent, i.e. that when applied on a given model, they will always produce a unique output model, independent of the order in which rules of the system are applied on the input. In this work, we consider Labelled Transition Systems (LTSs) to reason about the semantics of models, and LTS transformation systems to reason about model transformations. In related work, the problem of confluence detection has been investigated for general graph structures. We observe, however, that confluence can be detected more efficiently in special cases where the graphs have particular structural properties. In this paper, we present a number of observations to detect confluence of LTS transformation systems, and propose both a new confluence detection algorithm and a conflict resolution algorithm based on them.Comment: In Proceedings GaM 2015, arXiv:1504.0244

    Confluence reduction for Markov automata (extended version)

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    Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models generated by such specifications. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep these models small. We define the notion of confluence directly on Markov automata, and discuss how to syntactically detect confluence on the MAPA language as well. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude

    Boosting Fault Tree Analysis by Formal Methods

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    Consistently-detecting monitors

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    We study a contextual definition for deterministic monitoring based on consistent detections. It is defined in terms of the observed behaviour of the monitor when instrumented over arbitrary systems. We give an alternative, coinductive definition based on controllability which does not rely on system quantifications, and show that it is fully-abstract wrt. the former definition. We then develop a symbolic counterpart to the controllability definition to facilitate an automated analysis for controllable monitors involving data.peer-reviewe

    A comparison of confluence and ample sets in probabilistic and non-probabilistic branching time

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    Confluence reduction and partial order reduction by means of ample sets are two different techniques for state space reduction in both traditional and probabilistic model checking. This paper provides an extensive comparison between these two methods, and answers the question how they relate in terms of reduction power when preserving branching time properties. We prove that, while both preserve the same properties, confluence reduction is strictly more powerful than partial order reduction: every reduction that can be obtained with partial order reduction can also be obtained with confluence reduction, but the converse is not true. The main challenge for the comparison is that confluence reduction was defined in an action-based setting, whereas ample set reduction is often defined in a state-based setting. We therefore redefine confluence reduction in the state-based setting of Markov decision processes, and provide a nontrivial proof of its correctness. Additionally, we pinpoint precisely in what way confluence reduction is more general, and provide conditions under which the two notions coincide. The results we present also hold for non-probabilistic models, as they can just as well be applied in a context where all transitions are non-probabilistic. To discuss the practical applicability of our results, we adapt a state space generation technique based on representative states, already known in combination with confluence reduction, so that it can also be applied to ample sets

    13th international workshop on expressiveness in concurrency

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