2006 Formal Methods in Computer Aided Design
Bibliographic record
Abstract
The VLSI CAD flow encompasses an abundance of critical NP-complete and PSPACE-complete problems. Instead of developing a dedicated algorithm for each, the trend during the last decade has been to encode them in formal languages, such as Boolean satisfiability (SAT) and quantified Boolean formulas (QBFs), and focus academic resources on improving SAT and QBF solvers. The significant progress of these solvers has validated this strategy. This dissertation contributes to the further advancement of formal techniques in CAD. \n \nToday, the verification and debugging of increasingly complex RTL designs can consume up to 70% of the VLSI design cycle. In particular, RTL debug is a manual, resource-intensive task in the industry. The first contribution of this thesis is an in-depth examination of the factors affecting the theoretical computational complexity of debugging. It is established that most variations of the debugging problem are NP-complete. \n \nAutomated debugging tools return all potential error sources in the RTL, called solutions, that can explain a given failing error trace. Finding each solution requires a separate call to a formal engine, which is computationally expensive. \nThe second contribution of this dissertation comprises techniques for reducing the number of such iterations, by leveraging dominance relationships between RTL blocks to imply solutions. Extensive experiments on industrial designs show a three-fold reduction in the number of formal engine calls due to solution implications, resulting in a 1.64x overall speed-up. \n \nThe third contribution aims to advance the state-of-the-art of QBF solvers, whose progress has not been as impressive as that of SAT solvers. We present a framework for using complete dominators to preprocess and reduce QBFs with an inherent circuit structure, which is common in encodings of PSPACE-complete CAD problems. Experiments show that three modern QBF solvers together solve 55% of preprocessed QBF instances, compared to none without preprocessing. \n \nThe final contribution consists of a series of QBF encodings for evaluating the reconfigurability of partially programmable circuits (PPCs). The metrics of fault tolerance, design error tolerance and engineering change coverage are defined for PPCs and encoded using QBFs. These formulations along with experimental results demonstrate the theoretical and practical appropriateness of QBFs for dealing with reconfigurability.
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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 | 0.005 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.006 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.108 | 0.044 |
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".