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Towards Stronger Counterexamples to the Log-Approximate-Rank Conjecture
[article]
2020
arXiv
pre-print
We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on n input bits, each of which has approximate Fourier sparsity at most O(n^3) and randomized parity decision tree complexity Θ(n). This improves upon the recent work of Chattopadhyay, Mande and Sherif (JACM '20) both qualitatively (in terms of designing a large number of examples) and quantitatively (improving the gap from
arXiv:2009.02717v1
fatcat:extnblqgiff7xc66os6czqujzi