Bibliographic record
Abstract
We introduce a second-order theory V-Krom of bounded arithmetic for nondeterministic log space. This system is based on Gradel's characterization of NL by second-order Krom formulae with only universal first-order quantifiers, which in turn is motivated by the result that the decision problem for 2-CNF satisfiability is complete for coNL (and hence for NL). This theory has the style of the authors' theory Vi-Horn [APAL 124 (2003)] for polynomial time. Both theories use Zambella's elegant second-order syntax, and are axiomatized by a set 2-BASIC of simple formulae, together with a comprehension scheme for either second-order Horn formulae (in the case of V/sub 1/-Horn), or second-order Krom (2CNF) formulae (in the case of V-Krom). Our main result for V-Krom is a formalization of the Immerman-Szelepcsenyi theorem that NL is closed under complementation. This formalization is necessary to show that the NL functions are /spl Sigma//sub 1//sup B/-definable in V-Krom. The only other theory for NL in the literature relies on the Immerman-Szelepcsenyi's result rather than proving it.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".