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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > PARITY DECISION TREES:
Reports tagged with Parity Decision Trees:
TR14-115 | 27th August 2014
Roei Tell

Deconstructions of Reductions from Communication Complexity to Property Testing using Generalized Parity Decision Trees

Revisions: 1

A few years ago, Blais, Brody, and Matulef (2012) presented a methodology for proving lower bounds for property testing problems by reducing them from problems in communication complexity. Recently, Bhrushundi, Chakraborty, and Kulkarni (2014) showed that some reductions of this type can be deconstructed to two separate reductions, from communication ... more >>>


TR20-119 | 1st August 2020
Nikhil Mande, Swagato Sanyal

On parity decision trees for Fourier-sparse Boolean functions

We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Our contributions are as follows. Let $f : \mathbb{F}_2^n \to \{-1, 1\}$ be a Boolean function with Fourier support ... more >>>


TR22-173 | 3rd December 2022
Paul Beame, Sajin Koroth

On Disperser/Lifting Properties of the Index and Inner-Product Functions

Revisions: 1

Query-to-communication lifting theorems, which connect the query complexity of a Boolean function to the communication complexity of an associated `lifted' function obtained by composing the function with many copies of another function known as a gadget, have been instrumental in resolving many open questions in computational complexity. Several important complexity ... more >>>




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