Using Virus Machines to Compute Pairing Functions

Abstract

Virus machines are computational devices inspired by the movement of viruses between hosts and their capacity to replicate using the resources of the hosts. This behavior is controlled by an external graph of instructions that opens different channels of the system to make viruses capable of moving. This model of computation has been demonstrated to be as powerful as turing machines by different methods: by generating Diophantine sets, by computing partial recursive functions and by simulating register machines. It is interesting to investigate the practical use cases of this model in terms of possibilities and efficiency. In this work, we give the basic modules to create an arithmetic calculator. As a practical application, two pairing functions are calculated by means of two different virus machines. Pairing functions are important resources in the field of cryptography. The functions calculated are the Cantor pairing function and the Gödel pairing function.