On the Reliability of Computational Structures Using Majority Logic
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Bibliographic record
Abstract
The importance of the reliability of majority-based structures stems from their use in both conventional fault-tolerant architectures and emerging nanoelectronic systems. In this paper, analytical models are developed in order to gain a better understanding of the reliability of majority logic in these contexts. A minimally biased input scenario for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -input majority gates ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> odd) occurs when only a minimal majority of the inputs are in consensus. In a tree of gates with these inputs, this paper determines 1) that any nonzero error rate of the majority gates and/or of its initial inputs will result in an unreliable output and 2) that the use of majority gates with a larger number of inputs leads to a less reliable structure. These results are extended to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -input minority gates for odd <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> . Although these findings are based on tree structures, their implications to circuit design are explored by investigating several fault-tolerant and nanoelectronic architectures. The simulation results show that the increased probability of error in nanoscale devices may impose serious constraints on the reliability of emerging nanoelectronic circuits, as well as their fault-tolerant counterparts. The worst case reliability must be accounted for in a fault-tolerant design to ensure reliable operation.
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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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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