Relativized NP search problems and propositional proof systems
Bibliographic record
Abstract
An NP search problem is the problem of finding a witness to a given NP predicate, and TFNP is the class of total NP search problems. TFNP contains a number of subclasses containing natural problems; for example, PLS is the class of efficient local search heuristics. These classes are characterized by the combinatorial principle that guarantees the existence of a solution; for example, PLS is the class of such problems whose totality is assured by the principle "every dag with at least one edge has a sink". We show many strong connections between these search classes and the computational power - in particular the proof complexity - of their underlying principles. These connections, along with lower bounds in the propositional proof systems Nullstellensatz and bounded-depth LK, allow us to prove several new relative separations among PLS, and Papadimitriou's classes PPP, PPA, PPAD, and PPADS.
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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".