2026-07-22T21:29:53Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:10611 2024-03-06T10:46:16Z ddc:004 open_access

Query-To-Communication Lifting for BPP Using Inner Product Chattopadhyay, Arkadev Filmus, Yuval Koroth, Sajin Meir, Or Pitassi, Toniann lifting theorems inner product BPP Lifting Deterministic Lifting 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. [Arkadev Chattopadhyay et al., 2017] and Wu et al. [Xiaodi Wu et al., 2017]. The only query-to-communication lifting result for randomized protocols, due to Göös, Pitassi and Watson [Mika Göös et al., 2017], 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 [Mika Göös et al., 2017] 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Arkadev Chattopadhyay and Yuval Filmus and Sajin Koroth and Or Meir and Toniann Pitassi 2019 Is Part Of LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2019.35 urn:nbn:de:0030-drops-106110 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.35 eng https://creativecommons.org/licenses/by/3.0/legalcode