Amortized communication complexity of an equality predicate

TL;DR

This paper presents a new protocol for the equality predicate problem that reduces communication complexity to O(N) using pseudorandom generators and string synchronization, improving upon previous results from 1995.

Contribution

The paper introduces a novel protocol for the equality predicate with improved communication complexity, combining Nisan's pseudorandom generator and Smith's string synchronization.

Findings

Probabilistic communication complexity is O(N)

Protocol's computational complexity is polynomial in input size

Improves upon 1995 results by Feder et al.

Abstract

We study the communication complexity of a direct sum of independent copies of the equality predicate. We prove that the probabilistic communication complexity of this problem is equal to O(N); computational complexity of the proposed protocol is polynomial in size of inputs. Our protocol improves the result achieved in 1995(Feder, Kushilevitz, Naor, Nisan). Our construction is based on two techniques: Nisan's pseudorandom generator (1992) and Smith's string synchronization algorithm (2007).