Distribution-Free Testing of Decision Lists with a Sublinear Number of Queries

We give a distribution-free testing algorithm for decision lists with $\tilde{O}(n^{11\mathrm{/}12}\mathrm{/}{\epsilon }^3)$ queries. This is the first sublinear algorithm for this problem, which shows that, unlike halfspaces, testing is strictly easier than learning for decision lists. Complementing the algorithm, we show that any distribution-free tester for decision lists must make $\tilde{\mathrm{\Omega }}(\sqrt{n})$ queries, or draw $\tilde{\mathrm{\Omega }}(n)$ samples when the algorithm is sample-based.