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.

翻译：在这篇注记中，我们引入了由Kleinberg、Peale和Reingold（2026）提出的错误受限语言生成（MBLG）框架的多项式时间版本。我们观察到变量奇偶性族和文字合取族可在多项式时间内实现MBLG。我们的主要结果表明，具有多项式多个最大项（maxterm）的单调布尔函数族可在多项式时间内实现MBLG。该族包含所有可由多项式规模决策树计算的单调布尔函数。我们的技术可被呈现为一种关于在黑板（board）上书写数字的新型组合博弈。