Lower Bounds for Linear Decision Lists

Arkadev Chattopadhyay; Meena Mahajan; Nikhil Mande; Nitin Saurabh

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arXiv · 1901.05911

Lower Bounds for Linear Decision Lists

Arkadev Chattopadhyay·Meena Mahajan·Nikhil Mande·Nitin Saurabh

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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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BibTeX RIS

Arkadev Chattopadhyay, Meena Mahajan, Nikhil Mande, Nitin Saurabh. 2019-01-17. Lower Bounds for Linear Decision Lists. https://arxiv.org/abs/1901.05911

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