Space Lower Bounds for the Signal Detection Problem
Bibliographic record
Abstract
Abstract Many shared memory algorithms have to deal with the problem of determining whether the value of a shared object has changed in between two successive accesses of that object by a process when the responses from both are the same. Motivated by this problem, we define the signal detection problem , which can be studied on a purely combinatorial level. Consider a system with n + 1 processes consisting of n readers and one signaller. The processes communicate through a shared blackboard that can store a value from a domain of size m . Processes are scheduled by an adversary. When scheduled, a process reads the blackboard, modifies its contents arbitrarily, and, provided it is a reader, returns a Boolean value. A reader must return true if the signaller has taken a step since the reader’s preceding step; otherwise it must return false . Intuitively, in a system with n processes, signal detection should require at least n bits of shared information, i.e., m ≥ 2 n . But a proof of this conjecture remains elusive. For the general case, we prove a lower bound of m ≥ n 2 . For restricted versions of the problem, where the processes are oblivious or where the signaller must write a fixed sequence of values, we prove a tight lower bound of m ≥ 2 n . We also consider a version of the problem where each reader takes at most two steps. In this case, we prove that m = n + 1 blackboard values are necessary and sufficient.
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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 | 0.010 | 0.064 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.004 |
| Bibliometrics | 0.004 | 0.006 |
| Science and technology studies | 0.005 | 0.008 |
| Scholarly communication | 0.011 | 0.031 |
| Open science | 0.009 | 0.012 |
| Research integrity | 0.006 | 0.010 |
| Insufficient payload (model declined to judge) | 0.024 | 0.005 |
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".