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Electronic Colloquium on Computational Complexity

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TR25-133 | 12th September 2025
Pratik Shastri

Lower Bounds for Noncommutative Circuits with Low Syntactic Degree

Proving lower bounds on the size of noncommutative arithmetic circuits is an important problem in arithmetic circuit complexity. For explicit $n$ variate polynomials of degree $\Theta(n)$, the best known general bound is $\Omega(n \log n)$. Recent work of Chatterjee and Hrubeš has provided stronger ($\Omega(n^2)$) bounds for the restricted class ... more >>>


TR25-132 | 8th September 2025
Joshua Cook, Dana Moshkovitz

Time and Space Efficient Deterministic List Decoding

Error correcting codes encode messages by codewords in such a way that even if some of the codeword is corrupted, the message can be decoded. Typical decoding algorithms for error correcting codes either use linear space or quadratic time. A natural question is whether codes can be decoded in near-linear ... more >>>


TR25-131 | 7th September 2025
Anand Kumar Narayanan

Hyperdeterminants are hard in four dimensions

Hyperdeterminants are high dimensional analogues of determinants, associated with tensors of formats generalizing square matrices. First conceived for $2\times 2\times 2$ tensors by Cayley, they were developed in generality by Gelfand, Kapranov and Zelevinsky. Yet, hyperdeterminants in three or more dimensions are long conjectured to be VNP-Hard to compute, akin ... more >>>



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