We study the relationship between various one-way communication complexitymeasures of a composed function with the analogous decision tree complexity of the outer function . We consider two gadgets: the AND function on 2 inputs, and the Inner Product on a constant number of inputs . We show a lower bound on the VC-dimension of $f\circ IP$ and then appeal to a result of Klauck [STOC’00]. Our deterministiclower bound relies on a combinatorial result due to Frankl and Tokushige[Comb.’99]. For symmetric functions $f$, the non-adaptive AND decision-tree complexityof $f is at most quadratic in the (even two-way) communication complexity of$f \circ AND_2$. In view of the first point, a lower-bound on non-assistant AND decision treecomplexity of $F$ does not lift to a lowerbound on $f $f’s lower bound, the proof of first point above uses the well-studied Odd-Max-Bit function . The proof uses the Well-studying Odd-max-bit function. The proof of the last point above is based on the first and first point of the above and second point above using the Odd Max Bit function. It uses the OddMax Bit function to prove that the lower bound

Author(s) : Nikhil S. Mande, Swagato Sanyal

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Keywords : function - point - bound - decision - bit -

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