Published on Feb 20, 2020
A computer virus is a self-replicating program containing code that explicitly copies itself and that can "infect" other programs by modifying them or their environment such that a call to an infected program implies a call to a possibly evolved copy of the virus.
These software "pranks" are very serious; they are spreading faster than they are being stopped, and even the least harmful of viruses could be life-threatening. For example, in the context of a hospital life-support system, a virus that "simply" stops a computer and displays a message until a key is pressed, could be fatal. Further, those who create viruses can not halt their spread, even if they wanted to. It requires a concerted effort from computer users to be "virus-aware", rather than continuing the ambivalence that has allowed computer viruses to become such a problem.
Computer viruses are actually a special case of something known as "malicious logic" or "malware".
Consider the set of programs which produce one or more programs as output. For any pair of programs p and q, p eventually produces q if and only if p produces q either directly or through a series of steps (the "eventually produces" relation is the transitive closure of the "produces" relation.)
A viral set is a maximal set of programs V such that for every pair of programs p and q in V, p eventually produces q, and q eventually produces p. ("Maximal" here means that there is no program r not in the set that could be added to the set and have the set still satisfy the conditions.)
For the purposes of this paper, a computer virus is a viral set; a program p is said to be an instance of, or to be infected with, a virus V precisely when p is a member of the viral set V. A program is said to be infected simpliciter when there is some viral set V of which it is a member. A program which is an instance of some virus is said to spread whenever it produces another instance of that virus. The simplest virus is a viral set that contains exactly one program, where that program simply produces itself. Larger sets represent polymorphic viruses, which have a number of different possible forms, all of which eventually produce all the others.
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