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- W2950650152 abstract "We study the power of Arthur-Merlin probabilistic proof systems in the data stream model. We show a canonical $mathcal{AM}$ streaming algorithm for a wide class of data stream problems. The algorithm offers a tradeoff between the length of the proof and the space complexity that is needed to verify it. As an application, we give an $mathcal{AM}$ streaming algorithm for the emph{Distinct Elements} problem. Given a data stream of length $m$ over alphabet of size $n$, the algorithm uses $tilde O(s)$ space and a proof of size $tilde O(w)$, for every $s,w$ such that $s cdot w ge n$ (where $tilde O$ hides a $polylog(m,n)$ factor). We also prove a lower bound, showing that every $mathcal{MA}$ streaming algorithm for the emph{Distinct Elements} problem that uses $s$ bits of space and a proof of size $w$, satisfies $s cdot w = Omega(n)$. As a part of the proof of the lower bound for the emph{Distinct Elements} problem, we show a new lower bound of $Omega(sqrt n)$ on the $mathcal{MA}$ communication complexity of the emph{Gap Hamming Distance} problem, and prove its tightness." @default.
- W2950650152 created "2019-06-27" @default.
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- W2950650152 date "2013-02-02" @default.
- W2950650152 modified "2023-09-27" @default.
- W2950650152 title "Arthur-Merlin Streaming Complexity" @default.
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