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Record W2132910148 · doi:10.1109/sct.1989.41812

On the theory of average case complexity

2003· article· en· W2132910148 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

Venuenot available
Typearticle
Languageen
FieldComputer Science
TopicComplexity and Algorithms in Graphs
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsComplexity classNondeterministic algorithmTime complexityNPMathematicsComputational complexity theoryStructural complexity theoryEquivalence (formal languages)PHAverage-case complexityPSPACEExponential functionPolynomial hierarchyHierarchyDiscrete mathematicsDescriptive complexity theoryTime hierarchy theoremCounting problemContext (archaeology)Quantum complexity theoryAlgorithmTuring machineComputation

Abstract

fetched live from OpenAlex

Summary form only given, as follows. The authors take the next step in developing the theory of average case complexity initiated by L.A. Levin. Previous work has focused on the existence of complete problems. The present authors widen the scope to other basic questions in computational complexity. Their results include: (1) the equivalence of search and decision problems in the context of average case complexity; (2) an initial analysis of the structure of distributional-NP under reductions which preserve average polynomial-time; (3) a proof that if all distributional-NP is in average polynomial-time then nondeterministic exponential-time equals deterministic exponential time (i.e. a collapse in the worst-case hierarchy); and (4) definitions and basic theorems regarding other complexity classes such as average log space.

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: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.934
Threshold uncertainty score0.588

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.000

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 head0.060
GPT teacher head0.256
Teacher spread0.196 · 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

Quick stats

Citations36
Published2003
Admission routes1
Has abstractyes

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