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TR19-104 | 6th August 2019
Vishwas Bhargava, Shubhangi Saraf, Ilya Volkovich

Reconstruction of Depth-$4$ Multilinear Circuits

We present a deterministic algorithm for reconstructing multilinear $\Sigma\Pi\Sigma\Pi(k)$ circuits, i.e. multilinear depth-$4$ circuits with fan-in $k$ at the top $+$ gate. For any fixed $k$, given black-box access to a polynomial $f \in \mathbb{F}[x_{1},x_{2},\ldots ,x_{n}]$ computable by a multilinear $\Sigma\Pi\Sigma\Pi(k)$ circuit of size $s$, the algorithm runs in time ... more >>>

TR19-103 | 7th August 2019

Lifting theorems are theorems that relate the query complexity of a function $f:\left\{ 0,1 \right\}^n\to \left\{ 0,1 \right\}$ to the communication complexity of the composed function $f\circ g^n$, for some “gadget” $g:\left\{ 0,1 \right\}^b\times \left\{ 0,1 \right\}^b\to \left\{ 0,1 \right\}$. Such theorems allow transferring lower bounds from query complexity to ... more >>>

TR19-102 | 10th August 2019
Oded Goldreich

Testing Isomorphism in the Bounded-Degree Graph Model

Revisions: 1

We consider two versions of the problem of testing graph isomorphism in the bounded-degree graph model: A version in which one graph is fixed, and a version in which the input consists of two graphs.
We essentially determine the query complexity of these testing problems in the special case of ... more >>>

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