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The computational structure of progress conditions and shared objects

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Abstract

We study the effect of different progress conditions on the computability of distributed systems. For a system with n processes, we define exponentially many new progress conditions and explore their properties and relative strength. We cover many known and new interesting conditions and propose a new classification for evaluating the strength of shared objects. The classification is based on finding, for each object of type o, the strongest progress condition for which it is possible to solve consensus for any number of processes, using any number of objects of type o and atomic registers. Comparing our classification with the traditional one, which is based on fixing the progress condition (namely, wait-freedom) and finding the largest number of processes for which consensus is solvable, reveals interesting results. Together with our technical results, the new definitions provide a deeper understanding of synchronization and concurrency.

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Notes

  1. A swap operation takes as arguments a shared register and a local register, and atomically exchange their values.

  2. We notice that k-obstruction-freedom defined for a distinct system size is a distinct progress condition. By saying that it possible to solve consensus for any number of processes, assuming that the required progress condition is k-obstruction-freedom, we mean that it is possible to do so for any fixed number of processes n assuming that the required progress condition is k-obstruction-freedom for n processes.

  3. A test&set bit, say r, is a shared bit that supports two operations: (1) \( test \& set\), which writes 1 to r, and returns the old value (which is either 0 or 1); and (2) reset, which writes 0 into r (and does not return a value).

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Acknowledgements

I wish to thank the editor Eric Ruppert and three anonymous referees for their constructive comments and suggestions.

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  1. The Interdisciplinary Center, P.O.Box 167, 46150, Herzliya, Israel

    Gadi Taubenfeld

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Correspondence to Gadi Taubenfeld.

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Preliminary versions of the results presented in this paper appeared in: (1) the proceedings of the 13th international conf. on principles of distributed systems (OPODIS 2009, best paper award) [35], and (2) the proceedings of the 24th international symposium on distributed computing (DISC 2010) [36].

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Taubenfeld, G. The computational structure of progress conditions and shared objects. Distrib. Comput. 33, 103–123 (2020). https://doi.org/10.1007/s00446-019-00356-0

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