The Space Complexity of Scannable Objects with Bounded Components
Bibliographic record
Abstract
A fundamental task in the asynchronous shared memory model is obtaining a consistent view of a collection of shared objects while they are being modified concurrently by other processes. A scannable object addresses this problem. A scannable object is a sequence of readable objects called components, each of which can be accessed independently. It also supports the Scan operation, which simultaneously reads all of the components of the object. In this paper, we consider the space complexity of an n-process, k-component scannable object implementation from objects with bounded domain sizes. If the value of each component can change only a finite number of times, then there is a simple lock-free implementation from k objects. However, more objects are needed if each component is fully reusable, i.e. for every pair of values v, v', there is a sequence of operations that changes the value of the component from v to v'. We considered the special case of scannable binary objects, where each component has domain {0, 1}, in PODC 2021. Here, we present upper and lower bounds on the space complexity of any n-process implementation of a scannable object O with k fully reusable components from an arbitrary set of objects with bounded domain sizes. We construct a lock-free implementation from k objects of the same types as the components of O along with ⌈n/b⌉ objects with domain size 2^b. By weakening the progress condition to obstruction-freedom, we construct an implementation from k objects of the same types as the components of O along with ⌈n/(b-1)⌉ objects with domain size b. When the domain size of each component and each object used to implement O is equal to b and n ≤ b^k - bk + k, we prove that 1/2⋅ (k + (n-1)/b - log_b n) objects are required. This asymptotically matches our obstruction-free upper bound. When n > b^k - bk + k, we prove that 1/2⋅ (b^{k-1} - {(b-1)k + 1}/b) objects are required. We also present a lower bound on the number of objects needed when the domain sizes of the components and the objects used by the implementation are arbitrary and finite.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".