Minimum proof graphs and fastest-cut-first search heuristics
Bibliographic record
Abstract
Alpha-Beta is the most common game tree search algorithm, due to its high-performance and straightforward implementation. In practice one must find the best trade-off between heuristic evaluation time and bringing the subset of nodes explored closer to a minimum proof graph. In this paper we present a series of structural properties of minimum proof graphs that help us to prove that finding such graphs is NP-hard for arbitrary DAG inputs, but can be done in linear time for trees. We then introduce the class of fastest-cut-first search heuristics that aim to approximate minimum proof graphs by sorting moves based on approximations of sub-DAG values and sizes. To explore how various aspects of the game tree (such as branching factor and distribution of move values) affect the performance of Alpha-Beta we introduce the class of “Prefix Value Game Trees ” that allows us to label interior nodes with true minimax values on the fly without search. Using these trees we show that by explicitly attempting to approximate a minimum game tree we are able to achieve performance gains over Alpha-Beta with common extensions. 1
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 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".