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International Conference on Formal Modeling and Analysis of Timed Systems

FORMATS 2018: Formal Modeling and Analysis of Timed Systems pp 179–196Cite as

Non-bisimulation Based Behavioral Relations for Markov Automata

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11022))

Abstract

Markov automata (MAs) [16] extend probabilistic automata (PAs) [29] with stochastic aspects [22]. This paper defines two equivalence relations, namely, weighted Markovian equivalence (WME) and weak weighted Markovian equivalence (WWME) for the subclass of closed MAs. We define the quotient system under these relations and investigate their relationship with strong bisimulation and weak bisimulation, respectively. Next, we show that both WME and WWME can be used for repeated minimization of closed MAs. Finally, we prove that properties specified using deterministic timed automaton (DTA) specifications and metric temporal logic (MTL) formulas are preserved under WME and WWME quotienting.

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Notes

  1. 1.

    A MA is said to be closed if it is not subject to any further synchronization.

  2. 2.

    We restrict to models without zenoness. In simple words, this means that \(\tau \) cycles are not allowed.

  3. 3.

    Since our closed MA models do not allow multiple action transitions, schedulers are not required for resolving non-deterministic choices.

  4. 4.

    Note that the definition of strong bisimulation has been slightly modified to take into account the state labels.

  5. 5.

    For any MA \(\mathcal {M}\) and DTA \(\mathcal {A}\), the set \(Paths^{\mathcal {M}}(\mathcal {A})\) is measurable [11, 17, 33].

  6. 6.

    Note that paths satisfying an MTL formula \(\varphi \) can be written as a set of cylinder sets [33].

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Indian Institute of Science Education and Research Bhopal, Bhopal, India

    Arpit Sharma

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  1. Institute of Software, Chinese Academy of Sciences, Beijing, China

    David N. Jansen

  2. Kansas State University, Manhattan, Kansas, USA

    Pavithra Prabhakar

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Sharma, A. (2018). Non-bisimulation Based Behavioral Relations for Markov Automata. In: Jansen, D., Prabhakar, P. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2018. Lecture Notes in Computer Science(), vol 11022. Springer, Cham. https://doi.org/10.1007/978-3-030-00151-3_11

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  • DOI: https://doi.org/10.1007/978-3-030-00151-3_11

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