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 ... more >>>

We prove a lifting theorem from randomized decision tree depth to randomized parity decision tree (PDT) size. We use the same property of the gadget, stifling, which was introduced by Chattopadhyay, Mande, Sanyal and Sherif [ITCS'23] to prove a lifting theorem for deterministic PDTs. Moreover, even the milder condition that ... more >>>

We show that one-way functions exist if and only there exists an efficient distribution relative to which almost-optimal compression is hard on average. The result is obtained by combining a theorem of Ilango, Ren, and Santhanam [STOC 2022] and one by Bauwens and Zimand [JACM, 2023].

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