Formalization of Birth-Death and IID processes in higher-order logic
Bibliographic record
Abstract
Markov chains are extensively used in the modeling and analysis of engineering and scientific problems. Usually, paper-and-pencil proofs, simulation or computer algebra software are used to analyze Markovian models. However, these techniques either are not scalable or do not guarantee accurate results, which are vital in safety-critical systems. Probabilistic model checking has been proposed to formally analyze Markovian systems, but it suffers from the inherent state-explosion problem and unacceptable long computation times. Higher-order-logic theorem proving has been recently used to overcome the above-mentioned limitations but it lacks any support for discrete Birth-Death process and Independent and Identically Distributed (IID) random process, which are frequently used in many system analysis problems. In this paper, we formalize these notions using formal Discrete-Time Markov Chains (DTMC) with finite state-space and classified DTMCs in higher-order logic theorem proving. To demonstrate the usefulness of the formalizations, we present the formal performance analysis of two software applications.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| 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".