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Record W2404814723 · doi:10.7282/t31g0pdw

The Minimum Oracle Circuit Size Problem

2015· article· en· W2404814723 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

VenueView · 2015
Typearticle
Languageen
FieldComputer Science
TopicComputability, Logic, AI Algorithms
Canadian institutionsSimon Fraser University
Fundersnot available
KeywordsOracleCircuit complexityComplexity classKolmogorov complexityBounded functionVariety (cybernetics)Discrete mathematicsFunction (biology)Computer scienceMathematicsComputational complexity theoryRandom oracleCombinatoricsTime complexityAlgorithmElectronic circuitStatisticsPhysics

Abstract

fetched live from OpenAlex

We consider variants of the Minimum Circuit Size Problem MCSP, where the goal is to minimize the size of oracle circuits computing a given function. When the oracle is QBF, the resulting problem MCSP<sup>QBF</sup> is known to be complete for PSPACE under ZPP reductions. We show that it is not complete under logspace reductions, and indeed it is not even hard for TC<sup>0</sup> under uniform AC<sup>0</sup> reductions. We obtain a variety of consequences that follow if oracle versions of MCSP are hard for various complexity classes under different types of reductions. We also prove analogous results for the problem of determining the resource-bounded Kolmogorov complexity of strings, for certain types of Kolmogorov complexity measures.

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)0.001
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: Other design · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.955
Threshold uncertainty score0.645

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
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 science0.0020.001
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.001

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.

Opus teacher head0.049
GPT teacher head0.264
Teacher spread0.215 · 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