Space lower bounds for deterministic and randomized LL/SC implementations

Establish lower bounds on the space complexity of deterministic and randomized implementations of multiple LL/SC objects under the bounded-base-object model considered in the paper.

Background

The paper improves the known space complexity for randomized implementations of multiple LL/SC objects, obtaining an O(nτ+m) bound under a weak adaptive adversary. The conclusion identifies the absence of corresponding lower bounds for deterministic and randomized algorithms as an open research direction, which would clarify the optimality of the achieved space complexity.

References

Other open problems include finding lower bounds on space complexity for deterministic or even randomized algorithms, as well as a general construction for inserting \CL{} operations into implementations using LL/SC while preserving their asymptotic space complexity.

— Efficient Randomized LL/SC that Preserves History Independence  (2608.12946 - Bencivenga et al., 13 Aug 2026) in Section Conclusion

Another direction would be to determine whether our space complexity and/or QHI-preserving property is achievable with a strongly linearizable implementation, with a randomized algorithm under the strong adaptive adversary, with a deterministic algorithm, or under different attack models.

— Efficient Randomized LL/SC that Preserves History Independence  (2608.12946 - Bencivenga et al., 13 Aug 2026) in Section Conclusion