Enhanced covers of regular & indeterminate strings using prefix tables
Bibliographic record
Abstract
A \\itbf{cover} of a string x=x[1..n] is a proper substring u of x such that x can be constructed from possibly overlapping instances of u. A recent paper \\cite{FIKPPST13} relaxes this definition --- an \\itbf{enhanced cover} u of x is a border of x (that is, a proper prefix that is also a suffix) that covers a {\\it maximum} number of positions in x (not necessarily all) --- and proposes efficient algorithms for the computation of enhanced covers. These algorithms depend on the prior computation of the \\itbf{border array} β[1..n], where β[i] is the length of the longest border of x[1..i], 1≤i≤n. In this paper, we first show how to compute enhanced covers using instead the \\itbf{prefix table}: an array π[1..n] such that π[i] is the length of the longest substring of x beginning at position i that matches a prefix of x. Unlike the border array, the prefix table is robust: its properties hold also for \\itbf{indeterminate strings} --- that is, strings defined on {\\it subsets} of the alphabet Σ rather than individual elements of Σ. Thus, our algorithms, in addition to being faster in practice and more space-efficient than those of \\cite{FIKPPST13}, allow us to easily extend the computation of enhanced covers to indeterminate strings. Both for regular and indeterminate strings, our algorithms execute in expected linear time. Along the way we establish an important theoretical result: that the expected maximum length of any border of any prefix of a regular string x is approximately 1.64 for binary alphabets, less for larger ones
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".