Computational Model of Computer Virus

This paper points out some deficiencies in Adleman's model of computer virus. Some properties of computer virus are discussed and a new computational model of computer virus is developed which is based on the composition of function. A function v with number i=#(v) is infective iff ( ∞j∈P)(k∈P)(x∈N)[v(j)≠j Φ v(j) (x)=Φ kΦ i(x) (t∈P)Φ k(t)=t] With our model, we analyse some properties of computer virus and give the formal definitions of “benignant virus”,“malicious virus” and “mutating virus”. Comparing with other model of computer virus, our model is more practical and reasonable in respect of the computer virus' characters of infection and spread. We consider a function as a virus only if it is contagious. So,some functions without the feature of infection are not virus according to our model while they are virus in terms of Adleman's model. Such functions v:N→N are: 1. ( i,j∈N)[Φ v(i) (d,p)=Φ v(j) (d,p)] , here v(i)=v(j)=d . 2. x∈Nv(x)=x Comparing to Li Xiang's work, our model has the deficiency that our model is not suitable to describe the trigging condition of virus. In despite of this deficiency, we prove that the set of benignant virus in our model is the subset of unconditioned virus set in Li Xiang's model. However, there exists malicious virus in our model that is not a virus in term of Li Xiang's model.