Banach density reveals topological dichotomies in language generation: 1/2 is always achievable in 1D for finite-rank spaces but impossible in some infinite-rank cases, unlike asymptotic density; d>=2 needs nondegeneracy.
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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Banach density of generated languages: Dichotomies in topology and dimension
Banach density reveals topological dichotomies in language generation: 1/2 is always achievable in 1D for finite-rank spaces but impossible in some infinite-rank cases, unlike asymptotic density; d>=2 needs nondegeneracy.
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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.