XOR Lemmas for Communication via Marginal Information
Siddharth Iyer, Anup Rao

TL;DR
This paper introduces the concept of marginal information in communication protocols and proves XOR lemmas that relate the complexity and advantage of computing functions and their XORs, with implications for average-case and distribution-specific settings.
Contribution
It establishes new XOR lemmas based on marginal information, providing bounds on advantage for XOR functions in various communication complexity scenarios.
Findings
Exponential decay of advantage for XOR functions with increased protocol size
Near optimal bounds for product distributions and bounded-round protocols
Exponential bounds in the average case setting
Abstract
We define the of a communication protocol, and use it to prove XOR lemmas for communication complexity. We show that if every -bit protocol has bounded advantage for computing a Boolean function , then every -bit protocol has advantage for computing the -fold xor . We prove exponentially small bounds in the average case setting, and near optimal bounds for product distributions and for bounded-round protocols.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Cryptography and Data Security · semigroups and automata theory
