# Questions tagged [communication-complexity]

Questions regarding the amount of communication needed to accomplish a computational task, when the information about the task is spread across several agents

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### Descriptive complexity of communication complexity classes

It is well known that some major complexity classes, like P or NP, admit a full logical characterization (e.g NP = existential 2nd order logic by Fagin's theorem). On the other hand, one can also ...
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### Set Intersection lower bounds

Consider $S_1, ...,S_n \subseteq [U]$ where size of $U$ is polylogarithmic in $n$. We allow infinite time to pre-process these sets and then ask queries of the form $S_i \cap S_j$ is empty or not. We ...
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### Communication Complexity with real numbers

I'm looking into communication complexity with real numbers. One problem if we want to define this is that one can encode many real numbers $0.a_1a_2a_3... , 0.b_1b_2b_3..., 0.c_1c_2c_3...$ using only ...
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### Known upper bounds on the communication complexity of Karchmer-Wigderson games

In 1988 Karchmer and Wigderson established a nice characterization of the circuit depth $d$ (DeMorgan circuits) of a Boolean function $f \colon \{0,1\}^n\rightarrow\{0,1\}$: $d$ is exactly the number ...
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### Communication complexity of random functions with limited independence

Let $X_0, \ldots, X_{2^n-1}$ be $k$-wise independent random $0/1$ variables over a sample space $\Omega$ and $Prob \left[ X_i = 1 \right] = p$ for every $i$ and some $0 < p < 1$. Let assume $n$ ...
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### Number of $0/1$-monochromatic rectangles and communication complexity

What is the relation between number $0$-monochromatic rectangles in characteristic matrix and communication complexity? What is the relation between number $1$-monochromatic rectangles in ...
113 views

### On a possible probabilistic log-rank conjecture

The communication matrix of a function $f$ is a $2^{n}\times 2^{n}$ matrix $M_f$ where the indices of the rows (columns) correspond to the inputs of Alice (Bob), and each entry $M_f (a,b)$ is the ...
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### Modern tools deterministic communication applications

Partition number, Fooling-set method along with rank method provide important tools to identify deterministic communication complexity of a function. These techniques were identified some decades ...
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### Are there efficient black-box constructions of sigma-protocols for SAT?

Is there a known black-box construction for the following implication? non-interactive string commitment that stretches additively by an amount which does not depend on the string being ...
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### Deterministic one way communication complexity for message with arbitrary length

Let Alice have a binary string of length $n$ that it wants to send to Bob along a one-bit communication channel. However, Bob does not know the length of the message. I have been looking into ...