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The complexity of automated addition of fault-tolerance without explicit legitimate states

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Abstract

Existing algorithms for automated model repair for adding fault-tolerance to fault-intolerant models incur an impediment that designers have to identify the set of legitimate states of the original model. This set determines states from where the original model meets its specification in the absence of faults. Experience suggests that of the inputs required for model repair, identifying such legitimate states is the most difficult. In this paper, we consider the problem of automated model repair for adding fault-tolerance where legitimate states are not explicitly given as input. We show that without this input, in some instances, the complexity of model repair increases substantially (from polynomial-time to NP-complete). In spite of this increase, we find that this formulation is relatively complete; i.e., if it was possible to perform model repair with explicit legitimate states, then it is also possible to do so without the explicit identification of the legitimate states. Finally, we show that if the problem of model repair can be solved with explicit legitimate states, then the increased cost of solving it without explicit legitimate states is very small. In summary, the results in this paper identify instances of automated addition of fault-tolerance, where the explicit knowledge of legitimate state is beneficial and where it is not very crucial.

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Notes

  1. In total repair, the repaired model is expected to behave the same as the original model in the absence of faults. In partial repair, the set of behaviors of the repaired model is a subset of the set of behaviors of the original model in the absence of faults.

  2. We focus on leads-to properties, where holding a predicate must eventually be followed meeting another predicate.

  3. In prioritized synchronization, different processes have synchronized transitions and some have higher priority. Hence, not all interleavings are possible.

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Authors and Affiliations

  1. Department of Emergency Medicine, Yale University, 464 Congress Ave, Ste 260, New Haven, CT, 06519, USA

    Fuad Abujarad

  2. Department of Computing and Software, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canada

    Borzoo Bonakdarpour

  3. Department of Computer Science and Engineering, 3115 Engineering Building, East Lansing, MI, 48824, USA

    Yiyan Lin & Sandeep S. Kulkarni

Authors
  1. Fuad Abujarad
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  2. Yiyan Lin
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  3. Borzoo Bonakdarpour
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  4. Sandeep S. Kulkarni
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Corresponding author

Correspondence to Borzoo Bonakdarpour.

Additional information

This work was partially sponsored by Canada NSERC Discovery Grant 418396-2012 and NSERC Strategic Grant 430575-2012, US Air Force Contract FA9550-10-1-0178, and NSF CNS 0914913.

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Abujarad, F., Lin, Y., Bonakdarpour, B. et al. The complexity of automated addition of fault-tolerance without explicit legitimate states. Distrib. Comput. 28, 201–219 (2015). https://doi.org/10.1007/s00446-014-0227-2

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