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Revision #1 to TR24-203 | 30th May 2025 22:10

Direct Sums for Parity Decision Trees

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Revision #1 Authors: Tyler Besselman, Siyao Guo, Mika Göös, Gilbert Maystre, Weiqiang Yuan
Accepted on: 30th May 2025 22:10
Downloads: 18
Keywords: 


Abstract:

Direct sum theorems state that the cost of solving $k$ instances of a problem is at least $\Omega(k)$ times
the cost of solving a single instance. We prove the first such results in the randomised parity
decision tree model. We show that a direct sum theorem holds whenever (1) the lower bound for
parity decision trees is proved using the discrepancy method ; or (2) the lower bound is proved
relative to a product distribution.



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Paper:

TR24-203 | 9th December 2024 16:01

Direct Sums for Parity Decision Trees





TR24-203 Authors: Tyler Besselman, Mika Göös, Siyao Guo, Gilbert Maystre, Weiqiang Yuan
Publication: 12th December 2024 09:51
Downloads: 308
Keywords: 


Abstract:

Direct sum theorems state that the cost of solving $k$ instances of a problem is at least $\Omega(k)$ times
the cost of solving a single instance. We prove the first such results in the randomised parity
decision tree model. We show that a direct sum theorem holds whenever (1) the lower bound for
parity decision trees is proved using the discrepancy method ; or (2) the lower bound is proved
relative to a product distribution.


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