Identification via Functions

TL;DR

This paper introduces a new framework for root identification in noisy functions, establishing a logarithmic lower bound on observations that improves upon previous results and connects to message identification theory.

Contribution

It presents a novel logarithmic lower bound for root identification under noise, surpassing previous bounds and linking to message identification problems.

Findings

Established a new logarithmic lower bound on observations

Reproduced previous results as a special case

Connected root identification to message identification theory

Abstract

We develop a framework for studying the problem of identifying roots of a noisy function. We revisit a previous logarithmic bound on the number of observations and propose a general problem for identification of roots with three errors. As a key finding, we establish a novel logarithmic lower bound on the number of observations which outperforms the previous result across certain regimes of error and accuracy of the identification test. Furthermore, we recover the previous results for root identification as a special case and draw a connection to the message identification problem of Ahlswede.