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Revision #2 to TR20-054 | 5th November 2020 16:12

Communication Complexity with Defective Randomness

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Revision #2
Authors: Marshall Ball, Oded Goldreich, Tal Malkin
Accepted on: 5th November 2020 16:12
Downloads: 32
Keywords: 


Abstract:

Starting with the two standard model of randomized communication complexity, we study the communication complexity of functions when the protocol has access to a defective source of randomness.
Specifically, we consider both the public-randomness and private-randomness cases, while replacing the commonly postulated perfect randomness with distributions over $\ell$ bit strings that have min-entropy at least $k\leq\ell$.
We present general upper and lower bounds on the communication complexity in these cases, where the bounds are typically linear in $\ell-k$ and also depend on the size of the fooling set for the function being computed and on its standard randomized complexity.



Changes to previous version:

Correcting some typos and adding a reference.


Revision #1 to TR20-054 | 4th November 2020 09:27

Communication Complexity with Defective Randomness





Revision #1
Authors: Marshall Ball, Oded Goldreich, Tal Malkin
Accepted on: 4th November 2020 09:27
Downloads: 19
Keywords: 


Abstract:

Starting with the two standard model of randomized communication complexity, we study the communication complexity of functions when the protocol has access to a defective source of randomness.
Specifically, we consider both the public-randomness and private-randomness cases, while replacing the commonly postulated perfect randomness with distributions over $\ell$ bit strings that have min-entropy at least $k\leq\ell$.
We present general upper and lower bounds on the communication complexity in these cases, where the bounds are typically linear in $\ell-k$ and also depend on the size of the fooling set for the function being computed and on its standard randomized complexity.



Changes to previous version:

Correcting some typos.


Paper:

TR20-054 | 22nd April 2020 22:02

Communication Complexity with Defective Randomness





TR20-054
Authors: Marshall Ball, Oded Goldreich, Tal Malkin
Publication: 22nd April 2020 22:02
Downloads: 219
Keywords: 


Abstract:

Starting with the two standard model of randomized communication complexity, we study the communication complexity of functions when the protocol has access to a defective source of randomness.
Specifically, we consider both the public-randomness and private-randomness cases, while replacing the commonly postulated perfect randomness with distributions over $\ell$ bit strings that have min-entropy at least $k\leq\ell$.
We present general upper and lower bounds on the communication complexity in these cases, where the bounds are typically linear in $\ell-k$ and also depend on the size of the fooling set for the function being computed and on its standard randomized complexity.



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