The Complexity of Linear Temporal Verification for Continuous Counter Systems
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Bibliographic record
Abstract
Constant-rate multi-mode systems (MMSs) are hybrid systems with finitely many modes and real-valued variables that evolve over continuous time according to mode-specific constant rates. Equivalently, they correspond to continuous vector addition systems (VASs), where counters may become negative. We introduce a variant of linear temporal logic (LTL) for MMS, and we investigate the complexity of the model-checking problem for syntactic fragments of LTL. We obtain a complexity trichotomy: Each fragment is either P-complete, NP-complete, or undecidable. Since our logic can constrain the counters to remain non-negative, it further applies to continuous VAS. Thus, our results yield a framework for MMS and continuous VAS that generalizes and unify several existing results.
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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 | 0.000 |
| Open science | 0.001 | 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