A note on hardness of computing recursive teaching dimension

Pasin Manurangsi

Abstract: Highlights•Study computational complexity of recursive teaching dimension (RTD) when the concept class is given explicitly as input.•Brute-force algorithm computes RTD in nO(logn)<math><msup is="true"><mrow is="true"><mi is="true">n</mi></mrow><mrow is="true"><mi is="true">O</mi><mo stretchy="false" is="true">(</mo><mi is="true">l</mi><mi is="true">o</mi><mi is="true">g</mi><mi is="true">n</mi><mo stretchy="false" is="true">)</mo></mrow></msup></math> time.•We prove that, assuming the exponential time hypothesis (ETH), there is no no(logn)<math><msup is="true"><mrow is="true"><mi is="true">n</mi></mrow><mrow is="true"><mi is="true">o</mi><mo stretchy="false" is="true">(</mo><mi is="true">l</mi><mi is="true">o</mi><mi is="true">g</mi><mi is="true">n</mi><mo stretchy="false" is="true">)</mo></mrow></msup></math>-time algorithm for computing RTD.