Polynomial-Time Mistake-Bounded Language Generation

Abstract:In this note, we introduce a polynomial-time version of the mistake-bounded language generation (MBLG) framework due to Kleinberg, Peale, and Reingold (2026). We observe that the family of parities of variables, and the family of conjunctions of literals, are polynomial-time MBLG. Our main result states that the family of monotone Boolean functions with polynomially-many maxterms is polynomial-time MBLG. This family includes all monotone Boolean functions, computable by polynomial-size decision trees. Our technique can be presented as a new combinatorial game about writing numbers on a board.

Computational Complexity (cs.CC); Machine Learning (cs.LG)

arXiv:2606.16077 [cs.CC]

(or arXiv:2606.16077v1 [cs.CC] for this version)

https://doi.org/10.48550/arXiv.2606.16077 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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