Testability of generalized multiple-valued Reed-Muller circuits
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Bibliographic record
Abstract
The testability of generalized Reed-Muller circuits realizing m-valued functions in module m sum-of-product form, with m being a prime greater than two, is investigated. Two aspects of the problem are considered-the number of tests required for fault detection, and the generation of tests. We prove that just four tests are sufficient to detect all single stuck-at faults on internal lines in the circuit. Furthermore, this set of tests is independent of the function being realized and therefore universal. We give two alternative techniques for testing primary inputs-one by generating a test set of maximum length 2n, where n is the number of primary inputs and the other by adding to the circuit an extra multiplication mod m gate with an observable output to ensure that the four tests for internal lines also detect all single stuck-at faults on primary inputs.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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