Polynomial-Time Mistake-Bounded Language Generation

Héctor Jimenez; Alexander Kozachinskiy; Vicente Opazo

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arXiv · 2606.16077

Polynomial-Time Mistake-Bounded Language Generation

Héctor Jimenez·Alexander Kozachinskiy·Vicente Opazo

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Abstract

In this paper, we introduce a polynomial-time version of the mistake-bounded language generation (MBLG) framework due to Kleinberg, Peale, and Reingold (2026). We obtain upper and lower bounds for a number of simple families of Boolean functions. Namely, we first observe that families of parities of variables, symmetric functions and 2CNFs are polynomial-time MBLG. We then show that the family of monotone functions with polynomially-many maxterms is polynomial-time MBLG. For instance, disjunctions of literals are monotone Boolean functions with 1 maxterms, and thus polynomial-time MBLG. Under the strong RSA assumption, we show that disjunctions of literals are not polynomial-time MBLG. From the latter result, we deduce that polynomial-time MBLG families are not closed under union, and that there are families that are polynomial-time PAC learnable but not polynomial-time MBLG (again, under the strong RSA assumption). Finally, assuming existence of injective one-way functions, we show that there are polynomial-time MBLG families that are not polynomial-time PAC learnable.

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BibTeX RIS

Héctor Jimenez, Alexander Kozachinskiy, Vicente Opazo. 2026-06-15. Polynomial-Time Mistake-Bounded Language Generation. https://arxiv.org/abs/2606.16077

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