Under the stricter Banach-density measure, valid generation in the limit guarantees the optimal 1/2 coverage exactly when the language collection has finite Cantor-Bendixson rank; other collections force arbitrarily large sparse holes, and in dimension ≥ 2 geometry alone forces density zero.
Language generation in the limit: Noise, loss, and feedback
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Defines mistake-bounded generation and gives an algorithm for finite classes achieving optimal last-mistake time Cdim(L) with floor(log2 |L|) mistakes, plus a trade-off for infinite classes and noisy extensions.
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Validity, Sparse Holes, and Breadth in Language Generation: Banach Density, Topology, and Geometry
Under the stricter Banach-density measure, valid generation in the limit guarantees the optimal 1/2 coverage exactly when the language collection has finite Cantor-Bendixson rank; other collections force arbitrarily large sparse holes, and in dimension ≥ 2 geometry alone forces density zero.
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Mistake-Bounded Language Generation
Defines mistake-bounded generation and gives an algorithm for finite classes achieving optimal last-mistake time Cdim(L) with floor(log2 |L|) mistakes, plus a trade-off for infinite classes and noisy extensions.