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Record W2594960983

The Maximum Number of Runs in a String

2007· article· en· W2594960983 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
TopicAlgorithms and Data Compression
Canadian institutionsMcMaster University
Fundersnot available
KeywordsSubstringCombinatoricsMathematicsString (physics)Integer (computer science)ExponentPeriod (music)PrefixDiscrete mathematicsPhysicsData structureComputer science
DOInot available

Abstract

fetched live from OpenAlex

nor x[i−|u|..i−1] equals u. We say the repetition has period |u| and exponent e; it can be specified by the integer triple (i, |u|, e). It is well known [2] that the maximum number of repetitions in a string x = x[1..n] is Θ(n log n), and that the number of repetitions in x can be computed in Θ(n log n) time [2, 1, 10]. A string u is a run iff it is periodic of (minimum) period p ≤ |u|/2. Thus x = abaabaabaabaab = (aba)4ab is a run of period |aba| = 3. A substring u = x[i..j] of x is a run or maximal periodicity in x iff it is a run of period p and neither x[i−1..j] nor x[i..j+1] is a run of period p. The run u has exponent e = b|u|/pc and possibly empty tail t = x[i+ep..j] (proper prefix of x[i..i+p−1]). Thus

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: Other design · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.855
Threshold uncertainty score0.078

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 head0.011
GPT teacher head0.276
Teacher spread0.265 · 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

Citations9
Published2007
Admission routes1
Has abstractyes

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