Bibliographic record
Abstract
Trace theory (formulated by Mazurkiewicz in 1987) is a principled framework for defining equivalence relations for concurrent program runs based on a commutativity relation over the set of atomic steps taken by individual program threads. Its simplicity, elegance, and algorithmic efficiency makes it useful in many different contexts including program verification and testing. It is well-understood that the larger the equivalence classes are, the more benefits they would bring to the algorithms and applications that use them. In this paper, we study relaxations of trace equivalence with the goal of maintaining its algorithmic advantages. We first prove that the largest appropriate relaxation of trace equivalence, an equivalence relation that preserves the order of steps taken by each thread and what write operation each read operation observes, does not yield efficient algorithms. Specifically, we prove a linear space lower bound for the problem of checking, in a streaming setting, if two arbitrary steps of a concurrent program run are causally concurrent (i.e. they can be reordered in an equivalent run) or causally ordered (i.e. they always appear in the same order in all equivalent runs). The same problem can be decided in constant space for trace equivalence. Next, we propose a new commutativity-based notion of equivalence called grain equivalence that is strictly more relaxed than trace equivalence, and yet yields a constant space algorithm for the same problem. This notion of equivalence uses commutativity of grains , which are sequences of atomic steps, in addition to the standard commutativity from trace theory. We study the two distinct cases when the grains are contiguous subwords of the input program run and when they are not, formulate the precise definition of causal concurrency in each case, and show that they can be decided in constant space , despite being strict relaxations of the notion of causal concurrency based on trace equivalence.
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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 | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.001 | 0.006 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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".