Multiparty Communication Complexity of Finite Monoids
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Bibliographic record
Abstract
We study the relationship between the complexity of languages, in Yao’s two-party communication game and its extensions, and the algebraic properties of finite monoids that can recognize them. For a finite monoid M, we define C (k) (M) to be the maximum number of bits of communication that players need to exchange, in the k-party game of Chandra, Furst, and Lipton, to decide membership in any language recognized by M. We show that communication complexity classes induce pseudovarieties of finite monoids in a natural way and characterize some of them. Our results lead us to conjecture an extension of Szegedy’s algebraic characterization of languages having bounded two-party communication complexity. We also mention some applications of communication complexity lower bounds to circuit complexity.
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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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| 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 it