TY - GEN
T1 - Query-to-communication lifting for BPP using inner product
AU - Chattopadhyay, Arkadev
AU - Filmus, Yuval
AU - Koroth, Sajin
AU - Meir, Or
AU - Pitassi, Toniann
N1 - Publisher Copyright:
© Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, and Toniann Pitassi; licensed under Creative Commons License CC-BY
PY - 2019/7/1
Y1 - 2019/7/1
N2 - We prove a new query-to-communication lifting for randomized protocols, with inner product as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting. Prior to this work, such a theorem was known only for deterministic protocols, due to Chattopadhyay et al. [4] and Wu et al. [22]. The only query-to-communication lifting result for randomized protocols, due to Göös, Pitassi and Watson [13], used the much larger indexing gadget. Our proof also provides a unified treatment of randomized and deterministic lifting. Most existing proofs of deterministic lifting theorems use a measure of information known as thickness. In contrast, Göös, Pitassi and Watson [13] used blockwise min-entropy as a measure of information. Our proof uses the blockwise min-entropy framework to prove lifting theorems in both settings in a unified way.
AB - We prove a new query-to-communication lifting for randomized protocols, with inner product as gadget. This allows us to use a much smaller gadget, leading to a more efficient lifting. Prior to this work, such a theorem was known only for deterministic protocols, due to Chattopadhyay et al. [4] and Wu et al. [22]. The only query-to-communication lifting result for randomized protocols, due to Göös, Pitassi and Watson [13], used the much larger indexing gadget. Our proof also provides a unified treatment of randomized and deterministic lifting. Most existing proofs of deterministic lifting theorems use a measure of information known as thickness. In contrast, Göös, Pitassi and Watson [13] used blockwise min-entropy as a measure of information. Our proof uses the blockwise min-entropy framework to prove lifting theorems in both settings in a unified way.
KW - BPP Lifting
KW - Deterministic Lifting
KW - Inner product
KW - Lifting theorems
UR - http://www.scopus.com/inward/record.url?scp=85069185435&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2019.35
DO - 10.4230/LIPIcs.ICALP.2019.35
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AN - SCOPUS:85069185435
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
A2 - Baier, Christel
A2 - Chatzigiannakis, Ioannis
A2 - Flocchini, Paola
A2 - Leonardi, Stefano
T2 - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
Y2 - 9 July 2019 through 12 July 2019
ER -