Matrix Representation of Virus Machines

Virus machines are unconventional and bio-inspired models of computation based on the transmission of viruses among hosts. Virus machines are known to be computationally complete (they are algorithms), able to solve computationally hard problems. In this work we present a novel matrix representation for virus machines. Discrete structures such as vectors and matrices are useful in many technical domains, both in theory and practice. The hosts, number of viruses, and the instructions to control virus transmission are represented as vectors and matrices. In this way the computations of virus machines can be described by linear algebra operations. We also use our matrix representation to show invariants, helpful in formal verifications, of such machines.