Performance Analysis of Grammar-Based Codes Revisited
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Bibliographic record
Abstract
The compression performance of grammar-based codes is revisited from a new perspective. Previously, the compression performance of grammar-based codes was evaluated against that of the best arithmetic coding algorithm with finite contexts. In this correspondence, we first define semifinite-state sources and finite-order semi-Markov sources. Based on the definitions of semifinite-state sources and finite-order semi-Markov sources, and the idea of run-length encoding (RLE), we then extend traditional RLE algorithms to context-based RLE algorithms: RLE algorithms with k contexts and RLE algorithms of order k, where k is a nonnegative integer. For each individual sequence x, let r/sup *//sub sr,k/(x) and r/sup *//sub sr|k/(x) be the best compression rate given by RLE algorithms with k contexts and by RLE algorithms of order k, respectively. It is proved that for any x, r/sup *//sub sr,k/ is no greater than the best compression rate among all arithmetic coding algorithms with k contexts. Furthermore, it is shown that there exist stationary, ergodic semi-Markov sources for which the best RLE algorithms without any context outperform the best arithmetic coding algorithms with any finite number of contexts. Finally, we show that the worst case redundancies of grammar-based codes against r/sup *//sub sr,k/(x) and r/sup *//sub sr|k/(x) among all length- n individual sequences x from a finite alphabet are upper-bounded by d/sub 1/loglogn/logn and d/sub 2/loglogn/logn, respectively, where d/sub 1/ and d/sub 2/ are constants. This redundancy result is stronger than all previous corresponding results.
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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it