Robust Abstractions for Control Synthesis: Completeness via Robustness for Linear-Time Properties
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Bibliographic record
Abstract
We define robust abstractions for synthesizing provably correct and robust controllers for (possibly infinite) uncertain transition systems. It is shown that robust abstractions are sound in the sense that they preserve robust satisfaction of linear-time properties. We then focus on discrete-time control systems modelled by nonlinear difference equations with inputs and define concrete robust abstractions for them. While most abstraction techniques in the literature for nonlinear systems focus on constructing sound abstractions, we present computational procedures for constructing both sound and approximately complete robust abstractions for general nonlinear control systems without stability assumptions. Such procedures are approximately complete in the sense that, given a concrete discrete-time control system and an arbitrarily small perturbation of this system, there exists a finite transition system that robustly abstracts the concrete system and is abstracted by the slightly perturbed system simultaneously. A direct consequence of this result is that robust control synthesis for discrete-time nonlinear systems and linear-time specifications is robustly decidable. More specifically, if there exists a robust control strategy that realizes a given linear-time specification, we can algorithmically construct a (potentially less) robust control strategy that realizes the same specification. The theoretical results are illustrated with a simple motion planning example.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 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 it