Revisionist Simulations: A New Approach to Proving Space Lower Bounds
Bibliographic record
Abstract
Abstract. Determining the number of registers required for solving obstruction-free (or randomized wait-free) [Formula: see text]-set agreement is an open problem that highlights important gaps in our understanding of the space complexity of synchronization. The best known upper bound on the number of registers needed to solve this problem among [Formula: see text] processes is [Formula: see text] registers. No general lower bound better than 2 was known. We prove that any obstruction-free protocol solving [Formula: see text]-set agreement among [Formula: see text] processes must use at least [Formula: see text] registers. In particular, we get a tight lower bound of exactly [Formula: see text] registers for solving obstruction-free and randomized wait-free consensus. Our main tool is a simulation that serves as a reduction from the impossibility of deterministic wait-free [Formula: see text]-set agreement. In particular, we show that if an obstruction-free protocol for [Formula: see text]-set agreement uses fewer registers, then it is possible for [Formula: see text] processes to simulate the protocol and deterministically solve [Formula: see text]-set agreement in a wait-free manner, which is impossible. An important aspect of the simulation is the ability of simulating processes to revise the past of simulated processes. We introduce an augmented snapshot object, which facilitates this. More generally, our simulation applies to the broad class of colorless tasks. We can use it to prove, for example, a lower bound on the number of registers needed to solve obstruction-free [Formula: see text]-approximate agreement, which matches the best known upper bound to within a factor of 2 when [Formula: see text] is sufficiently small. No general lower bound for this problem was known. Finally, we prove that any lower bound on the number of registers used by obstruction-free protocols applies to protocols that satisfy nondeterministic solo-termination. Hence, our lower bounds for obstruction-free protocols also hold for randomized wait-free protocols.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.059 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.006 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.003 | 0.008 |
| Scholarly communication | 0.006 | 0.020 |
| Open science | 0.008 | 0.014 |
| Research integrity | 0.004 | 0.013 |
| Insufficient payload (model declined to judge) | 0.011 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".