Worst Case Branching and Other Measures of Nondeterminism
Bibliographic record
Abstract
Many nondeterminism measures for finite automata have been studied in the literature. The tree width of an NFA (nondeterministic finite automaton) counts the number of leaves of computation trees as a function of input length. The trace of an NFA is defined in terms of the largest product of the degrees of nondeterministic choices in computations on inputs of given length. Branching is the corresponding best case measure based on the product of nondeterministic choices in the computation that minimizes this value. We establish upper and lower bounds for the trace of an NFA in terms of its tree width. We give a tight bound for the size blow-up of determinizing an NFA with finite trace. Also we show that the trace of any NFA either is bounded by a constant or grows exponentially.
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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 | 0.005 | 0.056 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.005 | 0.013 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".