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[BMS+22] | Nathalie Bertrand,
Nicolas Markey,
Ocan Sankur, and
Nicolas Waldburger.
Parameterized safety verification of round-based
shared-memory systems.
In ICALP'22,
Leibniz International Proceedings in Informatics, pages 113:1-113:20. Leibniz-Zentrum für Informatik, July 2022.
- Abstract
We consider the parameterized verification problem for distributed algorithms where the goal is to develop techniques to prove the correctness of a given algorithm regardless of the number of participating processes. Motivated by an asynchronous binary consensus algorithm of [J. Aspnes; Fast deterministic consensus in a noisy environment; J. Algorithms, 2002], we consider round-based distributed algorithms communicating with shared memory. A particular challenge in these systems is that 1) the number of processes is unbounded, and, more importantly, 2) there is a fresh set of registers at each round. A verification algorithm thus needs to manage both sources of infinity. In this setting, we prove that the safety verification problem, which consists in deciding whether all possible executions avoid a given error state, is PSPACE-complete. For negative instances of the safety verification problem, we also provide exponential lower and upper bounds on the minimal number of processes needed for an error execution and on the minimal round on which the error state can be covered.
@inproceedings{icalp2022-BMSW, author = {Bertrand, Nathalie and Markey, Nicolas and Sankur, Ocan and Waldburger, Nicolas}, title = {Parameterized safety verification of round-based shared-memory systems}, editor = {Woodruff, David and Boja{\'n}czyk, Miko{\l}aj}, booktitle = {{P}roceedings of the 49th {I}nternational {C}olloquium on {A}utomata, {L}anguages and {P}rogramming ({ICALP}'22)}, acronym = {{ICALP}'22}, publisher = {Leibniz-Zentrum f{\"u}r Informatik}, series = {Leibniz International Proceedings in Informatics}, pages = {113:1-113:20}, year = {2022}, month = jul, doi = {10.4230/LIPIcs.ICALP.2022.113}, abstract = {We consider the parameterized verification problem for distributed algorithms where the goal is to develop techniques to prove the correctness of a given algorithm regardless of the number of participating processes. Motivated by an asynchronous binary consensus algorithm~of [J.~Aspnes; Fast deterministic consensus in a noisy environment; J.~Algorithms,~2002], we~consider round-based distributed algorithms communicating with shared memory. A~particular challenge in these systems is that 1)~the~number of processes is unbounded, and, more importantly, 2)~there is a fresh set of registers at each round. A~verification algorithm thus needs to manage both sources of infinity. In~this setting, we~prove that the safety verification problem, which consists in deciding whether all possible executions avoid a given error state, is PSPACE-complete. For~negative instances of the safety verification problem, we~also provide exponential lower and upper bounds on the minimal number of processes needed for an error execution and on the minimal round on which the error state can be covered.}, } |

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