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The Space Complexity of Approximating the Frequency Moments
TLDR
The frequency moments of a sequence containingmielements of typei, 1?i?n, are the numbersFk, when the elements of the sequence are given one by one and cannot be stored. Expand
The space complexity of approximating the frequency moments
TLDR
The frequency moments of a sequence containing mi elements of type i, for 1 i n, are the numbers Fk = P n=1 m k . Expand
Quantum speed-up of Markov chain based algorithms
  • M. Szegedy
  • Mathematics, Computer Science
  • 45th Annual IEEE Symposium on Foundations of…
  • 17 October 2004
TLDR
We develop a generic method for quantizing classical algorithms based on random walks. Expand
Proof verification and hardness of approximation problems
TLDR
The class PCP(f(n),g(n)) consists of all languages L for which there exists a polynomial-time probabilistic oracle machine that used O(f) random bits of its oracle and behaves as follows: If x in L then there exists an oracle y such that the machine accepts for all random choices but if x not in L the machine rejects with high probability. Expand
Proof verification and the hardness of approximation problems
TLDR
We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. Expand
On the degree of Boolean functions as real polynomials
TLDR
We characterize the degree of the polynomial representing a boolean function in terms of certain combinatorial properties of the boolean function. Expand
Checking computations in polylogarithmic time
Motivated by Manuel Blum’s concept of inst ante checking, we consider new, very fast and generic mechanisms of checking computations. Our results exploit recent advances in interactive proofExpand
Tracking join and self-join sizes in limited storage
TLDR
In this paper, we study algorithms for tracking (approximate) self-join sizes in limited storage in the presence of insertions and deletions to the relations. Expand
Multiparty Protocols, Pseudorandom Generators for Logspace, and Time-Space Trade-Offs
TLDR
We prove lower bounds of the form Ω(n · c−k), for the number of bits that need to be exchanged in order to compute some (explicitly given) polynomial time computable functions. Expand
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