Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
175 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Arthur-Merlin Streaming Complexity (1302.0418v1)

Published 2 Feb 2013 in cs.CC and cs.DS

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.

Citations (26)

Summary

We haven't generated a summary for this paper yet.