Computer viruses are programs that can replicate themselves by infecting other programs in a system. Bonfante, Kaczmarek and Marion have recently proposed a classification of viruses which relies on the recursion theory and its recursion theorems. We propose an extension of their formalism to consider in a more practical way the mutation of viruses. In particular, we are interested in modelling any depth of mutation, not just the first two levels. We show that this formalism still relies on recursion theorems, whatever the depth of mutation, even in the case of infinite depth. We also extend furthermore this formalism to model the viability of viral replication, which ensures that an infected program still can propagate the virus. An application of the proposed formalism to the class of combined viruses (multi-part viruses) is studied. Finally, given that metamorphic viruses can be modelled by grammars operating on grammars, we study a recursion-based approach of formal grammars and show that the recursion theorems of the recursion theory can be ported to the formal grammars theory.

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   |texte=   Extended Recursion-Based Formalization of Virus Mutation
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