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Electronic Colloquium on Computational Complexity

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All reports by Author Ankit Garg:

TR17-175 | 13th November 2017
Ankit Garg, Mika Göös, Pritish Kamath, Dmitry Sokolov

Monotone Circuit Lower Bounds from Resolution

Revisions: 1

For any unsatisfiable CNF formula $F$ that is hard to refute in the Resolution proof system, we show that a gadget-composed version of $F$ is hard to refute in any proof system whose lines are computed by efficient communication protocols---or, equivalently, that a monotone function associated with $F$ has large ... more >>>

TR17-162 | 26th October 2017
Klim Efremenko, Ankit Garg, Rafael Mendes de Oliveira, Avi Wigderson

Barriers for Rank Methods in Arithmetic Complexity

Arithmetic complexity, the study of the cost of computing polynomials via additions and multiplications, is considered (for many good reasons) simpler to understand than Boolean complexity, namely computing Boolean functions via logical gates. And indeed, we seem to have significantly more lower bound techniques and results in arithmetic complexity than ... more >>>

TR15-081 | 12th May 2015
Mark Braverman, Ankit Garg, Young Kun Ko, Jieming Mao, Dave Touchette

Near-optimal bounds on bounded-round quantum communication complexity of disjointness

We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r)$ on the communication required for computing disjointness of input size $n$, which is optimal up to logarithmic factors. The previous best lower bound ... more >>>

TR14-095 | 24th July 2014
Mark Braverman, Ankit Garg

Small value parallel repetition for general games

Revisions: 1

We prove a parallel repetition theorem for general games with value tending to 0. Previously Dinur and Steurer proved such a theorem for the special case of projection games. We use information theoretic techniques in our proof. Our proofs also extend to the high value regime (value close to 1) ... more >>>

TR13-130 | 17th September 2013
Mark Braverman, Ankit Garg

Public vs private coin in bounded-round information

Revisions: 1

We precisely characterize the role of private randomness in the ability of Alice to send a message to Bob while minimizing the amount of information revealed to him. We show that if using private randomness a message can be transmitted while revealing $I$ bits of information, the transmission can be ... more >>>

TR12-177 | 19th December 2012
Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein

Information lower bounds via self-reducibility

We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform ... more >>>

TR12-171 | 3rd December 2012
Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein

From Information to Exact Communication

We develop a new local characterization of the zero-error information complexity function for two party communication problems, and use it to compute the exact internal and external information complexity of the 2-bit AND function: $IC(AND,0) = C_{\wedge}\approx 1.4923$ bits, and $IC^{ext}(AND,0) = \log_2 3 \approx 1.5839$ bits. This leads to ... more >>>

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