Strongly Linearizable Implementations of Snapshots and Other Types
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Linearizability is the gold standard of correctness conditions for shared memory algorithms, and historically has been considered the practical equivalent of atomicity. However, it has been shown [1] that replacing atomic objects with linearizable implementations can affect the probability distribution of execution outcomes in randomized algorithms. Thus, linearizable objects are not always suitable replacements for atomic objects. A stricter correctness condition called strong linearizability has been developed and shown to be appropriate for randomized algorithms in a strong adaptive adversary model [1]. We devise several new lock-free strongly linearizable implementations from atomic registers. In particular, we give the first strongly linearizable lock-free snapshot implementation that uses bounded space. This improves on the unbounded space solution of Denysyuk and Woelfel [2]. As a building block, our algorithm uses a lock-free strongly linearizable ABA-detecting register. We obtain this object by modifying the wait-free linearizable ABA-detecting register of Aghazadeh and Woelfel [3], which, as we show, is not strongly linearizable. Aspnes and Herlihy [4] identified a wide class types that have wait-free linearizable implementations from atomic registers. These types require that any pair of operations either commute, or one overwrites the other. Aspnes and Herlihy gave a general wait-free linearizable implementation of such types, employing a wait-free linearizable snapshot object. Replacing that snapshot object with our lock-free strongly linearizable one, we prove that all types in this class have a lock-free strongly linearizable implementation from atomic registers.
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