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Hardness Amplification for Real-Valued Functions

Authors Yunqi Li , Prashant Nalini Vasudevan

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Average-case complexity
  • hardness amplification

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Abstract

Given an integer-valued function f:{0,1}ⁿ → {0,1,… , 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, … , x_t) = f(x_1) + ⋯ + f(x_t) is strongly hard to compute on instances (x_1,… ,x_t) drawn from the product distribution D^t. We also show the same for the task of approximately computing real-valued functions f:{0,1}ⁿ → [0,m). Our theorems immediately imply hardness self-amplification for several natural problems including Max-Clique and Max-SAT, Approximate #SAT, Entropy Estimation, etc..

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Yunqi Li and Prashant Nalini Vasudevan. Hardness Amplification for Real-Valued Functions. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 2:1-2:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CCC.2025.2

Author Details

Yunqi Li
  • Department of Computer Science, National University of Singapore, Singapore
Prashant Nalini Vasudevan
  • Department of Computer Science, National University of Singapore, Singapore

Funding

Both authors are supported by the National Research Foundation, Singapore, under its NRF Fellowship programme, award No. NRF-NRFF14-2022-0010.

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