Polynomial-Time Mistake-Bounded Language Generation

[2606.16077] Polynomial-Time Mistake-Bounded Language Generation Skip to main content Search Submit Donate Log in Computer Science > Computational Complexity arXiv:2606.16077 (cs) [Submitted on 15 Jun 2026 ( v1 ), last revised 22 Aug 2026 (this version, v2)] Title: Polynomial-Time Mistake-Bounded Language Generation Authors: Héctor Jimenez , Alexander Kozachinskiy , Vicente Opazo View PDF HTML (experimental) 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. Comments: v2 -- new results, including a lower bound for disjunction of literals, are added Subjects: Computational Complexity (cs.CC) ; Machine Learning (cs.LG) Cite as: arXiv:2606.16077 [cs.CC] (or arXiv:2606.16077v2 [cs.CC] for this version) https://doi.org/10.48550/arXiv.2606.16077 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Alexander Kozachinskiy [ view email ] [v1] Mon, 15 Jun 2026 00:31:11 UTC (9 KB) [v2] Sat, 22 Aug 2026 03:57:54 UTC (18 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.CC < prev | next > new | recent | 2026-06 Change to browse by: cs cs.LG References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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