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Electronic Colloquium on Computational Complexity

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All reports by Author Ron D. Rothblum:

TR21-127 | 30th August 2021
Ron D. Rothblum, Michael Ezra

Small Circuits Imply Efficient Arthur-Merlin Protocols

The inner product function $\langle x,y \rangle = \sum_i x_i y_i \bmod 2$ can be easily computed by a (linear-size) ${AC}^0(\oplus)$ circuit: that is, a constant depth circuit with AND, OR and parity (XOR) gates. But what if we impose the restriction that the parity gates can only be on ... more >>>

TR19-038 | 7th March 2019
Itay Berman, Akshay Degwekar, Ron D. Rothblum, Prashant Vasudevan

Statistical Difference Beyond the Polarizing Regime

Revisions: 1

The polarization lemma for statistical distance ($\mathrm{SD}$), due to Sahai and Vadhan (JACM, 2003), is an efficient transformation taking as input a pair of circuits $(C_0,C_1)$ and an integer $k$ and outputting a new pair of circuits $(D_0,D_1)$ such that if $\mathrm{SD}(C_0,C_1)\geq\alpha$ then $\mathrm{SD}(D_0,D_1) \geq 1-2^{-k}$ and if $\mathrm{SD}(C_0,C_1) \leq ... more >>>

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