A Classification of Viruses Through Recursion Theorems

We study computer virology from an abstract point of view. Viruses and worms are self-replicating programs, whose definitions are based on Kleene’s second recursion theorem. We introduce a notion of delayed recursion that we apply to both Kleene’s second recursion theorem and Smullyan’s double recursion theorem. This leads us to define four classes of viruses, two of them being polymorphic. Then, we work on a simple imperative programming language in order to show how those theoretical constructions can be implemented. In particular, we propose a general virus builder, and distribution engines. Topics covered. Computability theoretic aspects of programs, computer virology.