Modular Arithmetic Expressions and Primality Testing via DNA Self-Assembly

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.