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We are concerned with theoretical aspects of computer viruses. For this, we suggest a new definition of viruses which is clearly based on the iteration theorem and above all on Kleene's recursion theorem. We in this study capture in a natural way previous definitions, and in particular the one of Adleman. We establish generic virus constructions and we illustrate them by various examples. Lastly, we show the results on virus detection.doi:10.1007/s11416-005-0007-4 fatcat:qszvdv54qbbsvpuveicfrskvpa