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The SWMR ABD algorithm cannot emulate conditional write per se, but if the single writer is a stable leader, with a fault-tolerant leader election algorithm and appropriate modifications to the ABD algorithm (i.e. epoch counters in each message), it is possible to emulate conditional write, as shown in this industry paper: https://arxiv.org/abs/1702.04242.
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I only know that before “Primes in P” was shown, there were excellent non-deterministic algorithms to show whether a number is prime or composite (if the algorithm says “it’s prime” for a composite number, it’s 1000 times more likely due to a hardware problem than due to a problem with the algorithm).
I know of no efficient non-deterministic algorithm to ...
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