Tree Evaluation Is in Space đ (log đ · log log đ)
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The Tree Evaluation Problem (TreeEval) (Cook et al. 2009) is a central candidate for separating polynomial time (P) from logarithmic space (L) via composition. While space lower bounds of Ω(log2 n) are known for multiple restricted models, it was recently shown by Cook and Mertz (2020) that TreeEval can be solved in space O(log2 n/loglogn). Thus its status as a candidate hard problem for L remains a mystery. Our main result is to improve the space complexity of TreeEval to O(logn · loglogn), thus greatly strengthening the case that Tree Evaluation is in fact in L. We show two consequences of these results. First, we show that the KRW conjecture (Karchmer, Raz, and Wigderson 1995) implies L âNC1; this itself would have many implications, such as branching programs not being efficiently simulable by formulas. Our second consequence is to increase our understanding of amortized branching programs, also known as catalytic branching programs; we show that every function f on n bits can be computed by such a program of length Poly(n) and width 2O(n).
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frameâs 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.001 | 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 it