Fault-Tolerant Modular Reconstruction of Rational Numbers

TL;DR

This paper introduces two efficient algorithms for reconstructing rational numbers from multiple residue-modulus pairs, even when some residues are incorrect, enhancing fault tolerance in modular reconstruction processes.

Contribution

It generalizes existing methods to handle erroneous residues in rational number reconstruction, improving robustness and reliability of the process.

Findings

Algorithms effectively reconstruct rational numbers with faulty residues

Enhanced fault tolerance compared to previous methods

Applicable to various computational number theory problems

Abstract

In this paper we present two efficient methods for reconstructing a rational number from several residue-modulus pairs, some of which may be incorrect. One method is a natural generalization of that presented by Wang, Guy and Davenport in \cite{WGD1982} (for reconstructing a rational number from \textit{correct} modular images), and also of an algorithm presented in \cite{Abb1991} for reconstructing an \textit{integer} value from several residue-modulus pairs, some of which may be incorrect.