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Paper:

TR19-007 | 17th January 2019 18:32

Lower Bounds for Linear Decision Lists

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TR19-007
Authors: Arkadev Chattopadhyay, Meena Mahajan, Nikhil Mande, Nitin Saurabh
Publication: 17th January 2019 18:40
Downloads: 199
Keywords: 


Abstract:

We demonstrate a lower bound technique for linear decision lists, which are decision lists where the queries are arbitrary linear threshold functions.
We use this technique to prove an explicit lower bound by showing that any linear decision list computing the function $MAJ \circ XOR$ requires size $2^{0.18 n}$. This completely answers an open question of Tur{\'a}n and Vatan [FoCM'97]. We also show that the spectral classes $PL_1, PL_\infty$, and the polynomial threshold function classes $\widehat{PT}_1, PT_1$, are incomparable to linear decision lists.



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