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Record W2404946359

Repetition Complexity of Words.

2002· article· en· W2404946359 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

VenueDCFS · 2002
Typearticle
Languageen
FieldComputer Science
Topicsemigroups and automata theory
Canadian institutionsWestern University
Fundersnot available
KeywordsRepetition (rhetorical device)De Bruijn sequenceWord (group theory)MathematicsLogarithmComputational complexity theoryIterated functionTime complexityComplexity classCombinatoricsPrefixDiscrete mathematicsMorphismCombinatorics on wordsArithmeticAlgorithm
DOInot available

Abstract

fetched live from OpenAlex

With ideas from data compression and combinatorics on words, we introduce a complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word. The repetition complexity of w, r(w), is defined as the smallest amount of space needed to store w when reduced by repeatedly applying the following procedure: n consecutive occurrences uu . . . u of the same subword u of w are stored as (u, n). The repetition complexity has interesting relations with well-known complexity measures, such as subword complexity, sub, and Lempel-Ziv complexity, lz. We have always r(w) = lz(w) and could even be that the former is linear while the latter is only logarithmic; e.g., this happens for prefixes of certain infinite words obtained by iterated morphisms. An infinite word a being ultimately periodic is equivalent to: (i) sub(prefn(�)) = O(n), (ii) lz(prefn(�)) = O(1), and (iii) r(prefn(�)) = lgn + O(1). De Bruijn words, well known for their high subword complexity are shown to have almost highest repetition complexity; the precise complexity remains open. r(w) can be computed in time O(n3(log n)2) and it is open, and probably very difficult, to find very fast algorithms.

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 score0.652
Threshold uncertainty score0.269

Codex and Gemma teacher scores by category

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

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 head0.048
GPT teacher head0.230
Teacher spread0.182 · 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