MétaCan
Menu
Back to cohort
Record W2407080619

Low uniform versions of NC1.

2011· article· en· W2407080619 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueElectronic colloquium on computational complexity · 2011
Typearticle
Languageen
FieldComputer Science
Topicsemigroups and automata theory
Canadian institutionsUniversité de Montréal
Fundersnot available
KeywordsCharacterization (materials science)LogarithmPower (physics)Electronic circuitMathematicsComputer scienceValue (mathematics)Word (group theory)Discrete mathematicsCombinatoricsAlgorithmTopology (electrical circuits)GeometryPhysicsMathematical analysis
DOInot available

Abstract

fetched live from OpenAlex

In the setting known as DLOGTIME-uniformity, the fundamental complexity classes AC ⊂ ACC ⊆ TC ⊆ NC have several robust characterizations. In this paper we refine uniformity further and examine the impact of these refinements on NC and its subclasses. When applied to the logarithmic circuit depth characterization of NC, some refinements leave NC unchanged while others collapse NC to NC. Thus we study refinements of other circuit characterizations of NC. In the case of the AC(A5) characterization of NC , where A5 is the NC-complete word problem of the group A5, our refinements collapse NC to a subset of the regular languages. For the AC(D+) characterizations of NC, where D+ is the NC-complete language capturing the formula value problem, interestingly, these refinements scale down to circuits with linear fan-in. In particular, the latter refinements bring to the fore two classes, denoted FO[<]-uniform AC(D+)LIN and FO[<]uniform TCLIN , whose separation may be within the reach of current lower bound techniques, and whose separation would amount to distinguishing the power of a MAJ gate from that of a D+ gate.

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.704
Threshold uncertainty score0.748

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.036
GPT teacher head0.245
Teacher spread0.209 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it