Computability Theory deals with one of the most fundamental questions in computer science: What is computing and what are the limits of what a computer can compute? Or, formulated differently: "What kind of problems can be algorithmically solved?" During the course this question will be studied. Firstly, the notion of algorithm or computing will be made precise by using the mathematical model of a Turing machine. Secondly, it will be shown that basic issues in computer science, like "Given a program P does it halt for any input x?" or "Given two program P and Q, are they equivalent?" cannot be solved by any Turing machine. This shows that there exist problems that are impossible to solve with a computer, the so-called "undecidable problems".
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