arXiv:2606. 28354v1 Announce Type: cross Abstract: The classic paradigm of language identification in the limit models learning as a game between an adversary, who reveals strings from an unknown target language, and a learner tasked with identifying that language.
By Irene Strauss, Alexandra Butoi, Ryan Cotterell
arXiv:2608. 01320v1 Announce Type: cross Abstract: Language generation in the limit is a theoretical framework for studying how a generator can learn to produce new valid strings from a stream of positive examples.
By Ziyi Cai, Shuangping Li, Yiheng Shen, Kangning Wang, Peng Zhang
arXiv:2601. 21237v2 Announce Type: replace-cross Abstract: Kleinberg and Mullainathan recently proposed a formal framework for studying the phenomenon of language generation, called language generation in the limit.
By Aaron Li, Ian Zhang
arXiv:2606. 25777v1 Announce Type: cross Abstract: We initiate a resource-aware theory of \textit{language generation in the limit} under the minimal constraint of space efficiency.
By Nicolas Flammarion, Chirag Pabbaraju, Hristo Papazov, Miltiadis Stouras, Ola Svensson
The paper studies the problem of language generation in the limit, where a learner must produce valid unseen elements from any exhaustive positive presentation of an unknown infinite language. It establishes that generation is possible precisely when each target language admits a finite positive witness such that all targets activated by any finite sample share an infinite common intersection. The authors introduce a separation-width hierarchy to measure the size of compatible witnesses, showing that every level of the hierarchy occurs and that countable families admit singleton witnesses while more complex families require unbounded finite witnesses. The results are formalized and verified in Lean, with the development available on GitHub.
By Xiaoyu Li, Andi Han, Jiaojiao Jiang, Junbin Gao
arXiv:2601. 08648v2 Announce Type: replace-cross Abstract: Recent results in learning a language in the limit have shown that, although language identification is impossible, language generation is tractable.
By Antonios Anastasopoulos, Giuseppe Ateniese, Evgenios M. Kornaropoulos