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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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