Robust QBF Encodings for Sequential Circuits with Applications to Verification, Debug, and Test
Bibliographic record
Abstract
Formal CAD tools operate on mathematical models describing the sequential behavior of a VLSI design. With the growing size and state-space of modern digital hardware designs, the conciseness of this mathematical model is of paramount importance in extending the scalability of those tools, provided that the compression does not come at the cost of reduced performance. Quantified Boolean Formula satisfiability (QBF) is a powerful generalization of Boolean satisfiability (SAT). It also belongs to the same complexity class as many CAD problems dealing with sequential circuits, which makes it a natural candidate for encoding such problems. This work proposes a succinct QBF encoding for modeling sequential circuit behavior. The encoding is parametrized and further compression is achieved using time-frame windowing. Comprehensive hardware constructions are used to illustrate the proposed encodings. Three notable CAD problems, namely bounded model checking, design debugging and sequential test pattern generation, are encoded as QBF instances to demonstrate the robustness and practicality of the proposed approach. Extensive experiments on OpenCore circuits show memory reductions in the order of 90 percent and demonstrate competitive runtimes compared to state-of-the-art SAT techniques. Furthermore, the number of solved instances is increased by 16 percent. Admittedly, this work encourages further research in the use of QBF in CAD for VLSI.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".