Projectagon-based reachability analysis for circuit-level formal verification
Bibliographic record
Abstract
This dissertation presents a novel verification technique for analog and mixed signal circuits. Analog circuits are widely used in many applications include consumer electronics, telecommunications, medical electronics. Furthermore, in deep sub-micron design, physical effects might undermine common digital abstractions of circuit behavior. Therefore, it is necessary to develop systematic methodologies to formally verify hardware design using circuit-level models. We present a formal method for circuit-level verification. Our approach is based on translating verification problems to reachability analysis problems. It applies nonlinear ODEs to model circuit dynamics using modified nodal analysis. Forward reachable regions are computed from given initial states to explore all possible circuit behaviors. Analog properties are checked on all circuit states to ensure full correctness or find a design flaw. Our specification language extends LTL logic with continuous time and values and applies Brockett’s annuli to specify analog signals. We also introduced probability into the specification to support practical analog properties such as metastability behavior. We developed and implemented a reachability analysis tool COHO for a simple class of moderate-dimensional hybrid systems with nonlinear ODE dynamics. COHO employs projectagons to represent and manipulate moderate-dimensional, non-convex reachable regions. COHO solves nonlinear ODEs by conservatively approximating ODEs as linear differential inclusions. COHO is robust and efficient. It uses arbitrary precision rational numbers to implement exact computation and trims projectagons to remove infeasible regions. To improve performance and reduce error, several techniques are developed, including a guess-verify strategy, hybrid computation, approximate algorithms, and so on. The correctness and efficiency of our methods have been demonstrated by the success of verifying several circuits, including a toggle circuit, a flip-flop circuit, an arbiter circuit, and a ring-oscillator circuit proposed by researchers from Rambus Inc. Several important properties of these circuits have been verified and a design flaw was spotted during the toggle verification. During the reachability computation, we recognized new problems (e.g., stiffness) and proposed our solutions to these problems. We also developed new methods to analyze complex properties such as metastable behaviors. The combination of these methods and reachability analysis is capable of verifying practical circuits.
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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 | 0.002 | 0.005 |
| 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 | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".