DeepAI AI Chat
Log In Sign Up

A Composition Theorem via Conflict Complexity

by   Swagato Sanyal, et al.
Nanyang Technological University

Let (·) stand for the bounded-error randomized query complexity. We show that for any relation f ⊆{0,1}^n ×S and partial Boolean function g ⊆{0,1}^n ×{0,1}, _1/3(f ∘ g^n) = Ω(_4/9(f) ·√(_1/3(g))). Independently of us, Gavinsky, Lee and Santha newcomp proved this result. By an example demonstrated in their work, this bound is optimal. We prove our result by introducing a novel complexity measure called the conflict complexity of a partial Boolean function g, denoted by χ(g), which may be of independent interest. We show that χ(g) = Ω(√((g))) and (f ∘ g^n) = Ω((f) ·χ(g)).


page 1

page 2

page 3

page 4


A composition theorem for randomized query complexity via max conflict complexity

Let R_ϵ(·) stand for the bounded-error randomized query complexity with ...

The quantum query complexity of composition with a relation

The negative weight adversary method, ADV^±(g), is known to characterize...

Conflict complexity is lower bounded by block sensitivity

We show conflict complexity of any total boolean function, recently defi...

A Tight Composition Theorem for the Randomized Query Complexity of Partial Functions

We prove two new results about the randomized query complexity of compos...

Randomised Composition and Small-Bias Minimax

We prove two results about randomised query complexity R(f). First, we i...

On the randomised query complexity of composition

Let f⊆{0,1}^n×Ξ be a relation and g:{0,1}^m→{0,1,*} be a promise functio...

Level-p-complexity of Boolean functions using Thinning, Memoization, and Polynomials

This paper describes a purely functional library for computing level-p-c...