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We strengthen existing evidence for the so-called “algebrization barrier.” Algebrization—short for algebraic relativization—was introduced by Aaronson and Wigderson (AW) (STOC 2008) to characterize proofs involving arithmetization, simulation, and other “current techniques.” However, unlike...
We show that randomized communication complexity can be superlogarithmic in the partition number of the associated communication matrix, and we obtain near-optimal randomized lower bounds for the Clique versus Independent Set problem. These results strengthen the deterministic lower bounds...
We prove nearly matching upper and lower bounds on the randomized communication complexity of the following problem: Alice and Bob are each given a probability distribution over n elements, and they wish to estimate within ε the statistical (total variation) distance between their distributions....
Read-k oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ABP). In this work, we give an exponential lower bound of exp (n/kO(k)) on the width of any read-k oblivious ABP computing some explicit...
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