Towards a Classification of Behavioural Equivalences in Continuous-time Markov Processes
Bibliographic record
Abstract
Bisimulation is a concept that captures behavioural equivalence of states in a transition system. In [Linan Chen, Florence Clerc, and Prakash Panangaden, Bisimulation for feller-dynkin processes, in: Proceedings of the Thirty-Fifth Conference on the Mathematical Foundations of Programming Semantics, Electronic Notes in Theoretical Computer Science 347 (2019) 45–63.], we proposed two equivalent definitions of bisimulation on continuous-time stochastic processes where the evolution is a flow through time. In the present paper, we develop the theory further: we introduce different concepts that correspond to different behavioural equivalences and compare them to bisimulation. In particular, we study the relation between bisimulation and symmetry groups of the dynamics. We also provide a game interpretation for two of the behavioural equivalences. We then compare those notions to their discrete-time analogues.
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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 | 0.006 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.008 |
| Scholarly communication | 0.005 | 0.011 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".