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Electronic Colloquium on Computational Complexity

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TR22-165 | 22nd November 2022
Tsun-Ming Cheung, Hamed Hatami, Kaave Hosseini, Morgan Shirley

Separation of the factorization norm and randomized communication complexity

In an influential paper, Linial and Shraibman (STOC '07) introduced the factorization norm as a powerful tool for proving lower bounds against randomized and quantum communication complexities. They showed that the logarithm of the approximate $\gamma_2$-factorization norm is a lower bound for these parameters and asked whether a stronger ... more >>>


TR22-164 | 20th November 2022
Shuichi Hirahara, Mikito Nanashima

Learning versus Pseudorandom Generators in Constant Parallel Time

A polynomial-stretch pseudorandom generator (PPRG) in NC$^0$ (i.e., constant parallel time) is one of the most important cryptographic primitives, especially for constructing highly efficient cryptography and indistinguishability obfuscation. The celebrated work (Applebaum, Ishai, and Kushilevitz, SIAM Journal on Computing, 2006) on randomized encodings yields the characterization of sublinear-stretch pseudorandom generators ... more >>>


TR22-163 | 16th November 2022
Gil Cohen, Gal Maor

Random Walks on Rotating Expanders

Random walks on expanders are a powerful tool which found applications in many areas of theoretical computer science, and beyond. However, they come with an inherent cost -- the spectral expansion of the corresponding power graph deteriorates at a rate that is exponential in the length of the walk. As ... more >>>



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