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Electronic Colloquium on Computational Complexity

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TR25-087 | 27th June 2025
Yunqi Li, Prashant Nalini Vasudevan

Hardness Amplification for Real-Valued Functions

Given an integer-valued function $f:\{0,1\}^n\rightarrow \{0,1,\dots, m-1\}$ that is mildly hard to compute on instances drawn from some distribution $D$ over $\{0,1\}^n$, we show that the function $g(x_1, \dots, x_t) = f(x_1) + \dots + f(x_t)$ is strongly hard to compute on instances $(x_1, \dots, x_t)$ drawn from the product ... more >>>


TR25-086 | 30th June 2025
Jiatu Li

An Introduction to Feasible Mathematics and Bounded Arithmetic for Computer Scientists

This note gives an in-depth discussion on feasible mathematics and bounded arithmetic with a focus on Cook's theory PV (STOC'75). We present an informal characterization of PV based on three intuitive postulates and formulate the Feasible Mathematics Thesis, which asserts the equivalence between this informal framework and the formal system ... more >>>


TR25-085 | 28th June 2025
Somnath Bhattacharjee, Mrinal Kumar, Shanthanu Rai, Varun Ramanathan, Ramprasad Saptharishi, Shubhangi Saraf

Constant-depth circuits for polynomial GCD over any characteristic

We show that the GCD of two univariate polynomials can be computed by (piece-wise) algebraic circuits of constant depth and polynomial size over any sufficiently large field, regardless of the characteristic. This extends a recent result of Andrews \& Wigderson who showed such an upper bound over fields of zero ... more >>>



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