Verifying global convergence for a digital phase-locked loop
Bibliographic record
Abstract
We present a verification of a digital phase-locked loop (PLL) using the SpaceEx hybrid-systems tool. In particular, we establish global convergence - from any initial state the PLL eventually reaches a state of phase and frequency lock. Having shown that the PLL converges to a small region, traditional methods of circuit analysis based on linear-systems theory can be used to characterize the response of the PLL when in lock. The majority of the verification involves modeling each component of the PLL with piece-wise linear differential inclusions. We show how non-linear transfer functions, quantization error, and other non-idealities can be included in such a model. A limitation of piece-wise linear inclusions is that the linear coefficients for each component must take on fixed values. For real designs, ranges will be specified for these components. We show how a key step of the verification can be generalized to handle interval values for the linear coefficients by using an SMT solver.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".