Computer-assisted proof of lower bounds on the randomized query complexity of certain read-once threshold functions

Abstract: In this work we prove lower bounds on the randomized decision tree complexity of several read-once threshold functions. A read-once threshold formula can be defined by a rooted tree, in which every internal node is labeled by a threshold function (with output 1 only when at least  out of  input bits are 1) and each leaf by a variable. We consider the randomized decision tree complexity of such functions, when the underlying tree is a uniform and balanced tree with all its internal nodes labeled by the same threshold function. We prove lower bounds of the form , where  is the depth of the tree, for certain values of and. The value of each parameter depends on the solution of a linear program, which is provided by computational methods.

Keywords: Decision trees, query complexity, randomized computation, lower bounds, read-once functions.

Title: Computer-assisted proof of lower bounds on the randomized query complexity of certain read-once threshold functions

Author: Nikos Leonardos

International Journal of Recent Research in Mathematics Computer Science and Information Technology

ISSN 2350-1022

Vol. 9, Issue 2, October 2022 - March 2023

Page No: 11-17

Paper Publications

Website: www.paperpublications.org

Published Date: 10-December-2022

DOI: https://doi.org/10.5281/zenodo.7421269

Paper Download Link (Source)

https://www.paperpublications.org/upload/book/Computer-assisted%20proof%20of%20lower-10122022-1.pdf