Under a random oracle, a countable family of infinite languages has closure dimension zero and admits zero-mistake unbounded generation, yet every polynomial-query generator incurs an exponential expected-mistake lower bound on some target.
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On Computational Hardness of Mistake-Bounded Language Generation: A Random-Oracle Query Separation
Under a random oracle, a countable family of infinite languages has closure dimension zero and admits zero-mistake unbounded generation, yet every polynomial-query generator incurs an exponential expected-mistake lower bound on some target.