Query-to-communication lifting for BPP using inner product
Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir and Toni Pitassi
ICALP'19, SICOMP
We prove a query-to-communication lifting theorem in both the deterministic and randomized settings, using inner product as the lifting gadget.
Our result improves on the lifting theorem of Göös, Pitassi and Watson for randomized protocols, which used the indexing gadget.
Moreover, we reprove the lifting theorem of Chattopadhyay, Koucký, Loff and Mukhopadhyay for deterministic protocols using inner product.
Whereas Chattopadhyay et al. proved their result using thickness as the pseudorandomness notion (following the seminal work of Raz and McKenzie), we are able to use blockwise min-entropy, the same pseudorandomness notion used by Göös et al. to prove their randomized lifting theorem.
@inproceedings{CFKMP2019,
title = {Query-to-communication lifting for {BPP} using inner product},
author = {Arkadev Chattopadhyay and Yuval Filmus and Sajin Koroth and Or Meir and Toniann Pitassi},
booktitle = {46th International Colloquium on Automata, Languages and Programming (ICALP'19)},
year = {2019}
}
@article{CFKMP2021,
title = {Query-to-communication lifting for {BPP} using inner product},
author = {Arkadev Chattopadhyay and Yuval Filmus and Sajin Koroth and Or Meir and Toniann Pitassi},
journal = {SIAM J. Comp.},
volume = {50},
number = {1},
pages = {171--210},
year = {2021}
}
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