Efficient Composited de Bruijn Sequence Generators
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Bibliographic record
Abstract
A binary de Bruijn sequence with period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> is a sequence in which every tuple of n bits occurs exactly once. De Bruijn sequence generators have randomness properties that make them attractive for pseudorandom number generators and as building blocks for stream ciphers. Unfortunately, it is very difficult to find de Bruijn sequence generators with long periods (e.g., 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">128</sup> ) and most known de Bruijn sequence generators are computationally quite expensive. In this article, we present “OcDeb-k-n” and the first hardware implementation of de Bruijn sequence generators. OcDeb-k-n efficiently computes a composited de Bruijn sequence where k levels of composition are added to a de Bruijn sequence of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> . Numerically, OcDeb reduces the bit operations used for computing the feedback function significantly from Θ(k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + nk) to Θ(k log k + logn). Furthermore, it enables efficient parallelization and hardware retiming. Comprehensive result analysis is conducted for 65 nm ASIC technology. For example, OcDeb-32-32 has an area of 643 GE with 1.45 Gbps performance, and with parallelization it generates up to 25.4 Gbps at the cost of 4,787 GE. The area of OcDeb-512-32 generating a de Bruijn sequence of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">544</sup> is 7,304 GE and the performance is 1.25 Gbps.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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