How to Teach the Undecidability of Malware Detection Problem and Halting Problem

Abstract : Malware detection is a term that is often associated to Computer Science Security. The underlying main problem is called Virus detection and consists in answering the following question: Is there a program that can always decide if a program is a virus or not? On the other hand, the undecidability of some problems is an important notion in Computer Science : an undecidable problem is a problem for which no algorithm exists to solve it. We propose an activity that demonstrates that virus detection is an undecidable problem. Hence we prove that the answer to the above question is no. We follow the proof given by Cohen in his PhD in 1983. The proof is close to the proof given by Turing in 1936 of the undecidability of the Halting problem. We also give an activity to prove the undecidability of the Halting problem. These proofs allow us to introduce two important ways of proving theorems in Computer Science : proof by contradiction and proof by case disjunction. We propose a simple way to present these notions to students using a maze. Our activity is unplugged, i.e. we use only a paper based model of computer , and is designed for high-school students. This is the reason why we use Scratch to write our "programs".