Modular Arithmetic Expressions and Primality Testing via DNA Self-Assembly

TL;DR

This paper introduces tile self-assembly methods for performing basic arithmetic, modular operations, and primality testing using DNA, along with software tools to facilitate these computations in molecular systems.

Contribution

It presents novel tile sets for multi-input arithmetic, modular operations, and primality testing, advancing DNA self-assembly computational capabilities.

Findings

Tile sets for addition, subtraction, multiplication of n inputs

Software 'xtilemod' for modular arithmetic computations

Tile set and software for primality testing

Abstract

Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for solving many mathematical and computational problems via tile self assembly have been proposed by many researchers in the last decade. In particular tile set for doing basic arithmetic of two inputs have been given. In this work we give tile set for doing basic arithmetic (addition, subtraction, multiplication) of n inputs and subsequently computing its modulo. We also present a tile set for primality testing. Finally we present a software 'xtilemod' for doing modular arithmetic. This simplifies the task of creating the input files to xgrow simulator for doing basic (addition, subtraction, multiplication and division) as well as modular arithmetic of n inputs. Similar software for creating tile set for primality testing is also given.