A set-theoretic model of a test structure for verifying in silicon libraries of standard digital elements
Bibliographic record
Abstract
Verification of silicon digital design kit is a critical task for semiconductor technologies across all scales. The transition to advanced submicron technologies has significantly heightened its relevance due to the escalating complexity and cost of VLSI design. This article presents the development of a set-theoretic model for a test structure aimed at verifying standard digital cell libraries. The proposed model formally describes the hierarchy of components, including elements under test (combinational and sequential), selection and control blocks, input stimulus generation blocks, signal output blocks, and auxiliary hierarchical blocks. The model enables the estimation of the number of inputs and outputs of the verification structure based on library characteristics, such as the number of elements, quantity and bit-width of inputs and outputs, and logical functions of the elements. The results of applying the model are demonstrated using industrial libraries with process nodes of 180 nm, 90 nm, and 28 nm. A 6.4-fold increase in the number of tested elements (from 199 to 1274) results in only a 1.3-fold growth in the total number of inputs/outputs (from 25 to 32), confirming the model’s efficiency. Particular emphasis is placed on reducing the test structure area while maintaining verification completeness.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".