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Electronic Colloquium on Computational Complexity

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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 >>>


TR22-112 | 12th August 2022
Shalev Ben-David, Eric Blais, Mika Göös, Gilbert Maystre

Randomised Composition and Small-Bias Minimax

We prove two results about randomised query complexity $\mathrm{R}(f)$. First, we introduce a linearised complexity measure $\mathrm{LR}$ and show that it satisfies an inner-optimal composition theorem: $\mathrm{R}(f\circ g) \geq \Omega(\mathrm{R}(f) \mathrm{LR}(g))$ for all partial $f$ and $g$, and moreover, $\mathrm{LR}$ is the largest possible measure with this property. In particular, ... more >>>



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