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A complexity-based classification for multiprocessor synchronization

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Abstract

For many years, Herlihy’s elegant computability-based Consensus Hierarchy has been our best explanation of the relative power of various objects. Since real multiprocessors allow the different instructions they support to be applied to any memory location, it makes sense to consider combining the instructions supported by different objects, rather than considering collections of different objects. Surprisingly, this causes Herlihy’s computability-based hierarchy to collapse. In this paper, we suggest an alternative: a complexity-based classification of the relative power of sets of multiprocessor synchronization instructions, captured by the minimum number of memory locations of unbounded size that are needed to solve obstruction-free consensus when using different sets of instructions.

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Acknowledgements

The authors would like to thank Yehuda Afek, Dan Alistarh, Michael Coulombe, Eli Gafni, Petr Kuznetsov, and Philipp Woelfel for helpful conversations and feedback. Part of this work was performed when Rati Gelashvili was a Ph.D. student at MIT. Support is gratefully acknowledged from the Natural Science and Engineering Research Council of Canada (NSERC) under Discovery Grant RGPIN-2015-05080 and a Postgraduate Scholarship, a University of Toronto Faculty of Arts and Science Postdoctoral Fellowship, the National Science Foundation under grants CCF-1217921, CCF-1301926, and IIS-1447786, the Department of Energy under grant ER26116/DE-SC0008923, and SUN Microsystems, Oracle and Intel corporations. A preliminary version of this paper appeared in [10].

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Authors and Affiliations

  1. University of Toronto, Toronto, Canada

    Faith Ellen, Rati Gelashvili & Leqi Zhu

  2. MIT, Cambridge, USA

    Nir Shavit

  3. Tel Aviv University, Tel Aviv, Israel

    Nir Shavit

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  1. Faith Ellen
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  2. Rati Gelashvili
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  3. Nir Shavit
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  4. Leqi Zhu
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Correspondence to Rati Gelashvili.

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Ellen, F., Gelashvili, R., Shavit, N. et al. A complexity-based classification for multiprocessor synchronization. Distrib. Comput. 33, 125–144 (2020). https://doi.org/10.1007/s00446-019-00361-3

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  • DOI: https://doi.org/10.1007/s00446-019-00361-3