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Electronic Colloquium on Computational Complexity

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TR22-115 | 17th August 2022
Dieter van Melkebeek, Andrew Morgan

Polynomial Identity Testing via Evaluation of Rational Functions

Revisions: 2

We introduce a hitting set generator for Polynomial Identity Testing
based on evaluations of low-degree univariate rational functions at
abscissas associated with the variables. Despite the univariate
nature, we establish an equivalence up to rescaling with a generator
introduced by Shpilka and Volkovich, which has a similar structure but
uses ... more >>>


TR22-114 | 16th August 2022
Hao Wu

Direct Sum Theorems From Fortification

Revisions: 1

We revisit the direct sum theorems in communication complexity which askes whether the resource to solve $n$ communication problems together is (approximately) the sum of resources to solve these problems separately. Our work starts with the observation that Meir and Dinur's fortification lemma for protocol size over rectangles can be ... more >>>


TR22-113 | 11th August 2022
Yanyi Liu, Rafael Pass

Leakage-Resilient Hardness v.s. Randomness

Revisions: 2

A central open problem in complexity theory concerns the question of
whether all efficient randomized algorithms can be simulated by
efficient deterministic algorithms. The celebrated ``hardness
v.s. randomness” paradigm pioneered by Blum-Micali (SIAM JoC’84),
Yao (FOCS’84) and Nisan-Wigderson (JCSS’94) presents hardness
assumptions under which $\prBPP = \prP$, but these hardness ... more >>>



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