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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > VENKATESAN GURUSWAMI:
All reports by Author Venkatesan Guruswami:

TR22-102 | 15th July 2022
Venkatesan Guruswami, Xin Lyu, Xiuhan Wang

Range Avoidance for Low-depth Circuits and Connections to Pseudorandomness

In the range avoidance problem, the input is a multi-output Boolean circuit with more outputs than inputs, and the goal is to find a string outside its range (which is guaranteed to exist). We show that well-known explicit construction questions such as finding binary linear codes achieving the Gilbert-Varshamov bound ... more >>>


TR22-101 | 15th July 2022
Omar Alrabiah, Venkatesan Guruswami, Pravesh Kothari, Peter Manohar

A Near-Cubic Lower Bound for 3-Query Locally Decodable Codes from Semirandom CSP Refutation

A code $C \colon \{0,1\}^k \to \{0,1\}^n$ is a $q$-locally decodable code ($q$-LDC) if one can recover any chosen bit $b_i$ of the message $b \in \{0,1\}^k$ with good confidence by randomly querying the encoding $x = C(b)$ on at most $q$ coordinates. Existing constructions of $2$-LDCs achieve $n = ... more >>>




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