Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Tight Lower Bounds for the Distinct Elements Problem
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
On the Power of Quantum Proofs
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Join-distinct aggregate estimation over update streams
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On synopses for distinct-value estimation under multiset operations
Proceedings of the 2007 ACM SIGMOD international conference on Management of data
Delegating computation: interactive proofs for muggles
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Algebrization: A New Barrier in Complexity Theory
ACM Transactions on Computation Theory (TOCT)
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A Multi-Round Communication Lower Bound for Gap Hamming and Some Consequences
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
An optimal algorithm for the distinct elements problem
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
An optimal lower bound on the communication complexity of gap-hamming-distance
Proceedings of the forty-third annual ACM symposium on Theory of computing
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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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 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 ·w≥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 Distinct Elements problem that uses s bits of space and a proof of size w, satisfies s ·w=Ω(n). As a part of the proof of the lower bound for the Distinct Elements problem, we show a new lower bound of $\Omega \left( \sqrt n \right )$ on the ${\mathcal{MA}}$ communication complexity of the Gap Hamming Distance problem, and prove its tightness.