Approximate Analysis of Probabilistic Processes: Logic, Simulation and Games
Bibliographic record
Abstract
We tackle the problem of non robustness of simulation and bisimulation when dealing with probabilistic processes. It is important to ignore tiny deviations in probabilities because these often come from experiments or estimations. A few approaches have been proposed to treat this issue, for example metrics to quantify the non bisimilarity (or closeness) of processes. Relaxing the definition of simulation and bisimulation is another avenue which we follow. We define a new semantics to a known simple logic for probabilistic processes and show that it characterises a notion of epsi-simulation. We also define two-players games that correspond to these notions: the existence of a winning strategy for one of the players determines epsi-(bi)simulation. Of course, for all the notions defined, letting epsi = 0 gives back the usual notions of logical equivalence, simulation and bisimulation. However, in contrast to what happens in fully probabilistic systems when epsi = 0, two-way e-simulation for epsi > 0 is not equal to epsi-bisimulation. Next we give a polynomial time algorithm to compute a naturally derived metric: distance between states s and t is defined as the smallest epsi such that s and t are epsi-equivalent. This is the first polynomial algorithm for a non-discounted metric. Finally we show that most of these notions can be extended to deal with probabilistic systems that allow non-determinism as well.
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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 | 0.003 | 0.013 |
| 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 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".