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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 what kind of problems can be algorithmically solved? During the course, this question will be studied. The notion of algorithm or computing will be made precise by using the mathematical model of a Turing machine throughout this course.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: TU Delft

Course Curriculum

Module: 01
1. Preliminaries – Automata and Languages 00:05:00
Module: 02
2.A. The Turing machine 00:05:00
2.B. Variants of Turing machines 00:05:00
2.C. Non-deterministic Turing machines and their equivalence to ordinary Turing machines 00:05:00
2.D. Enumerators and Hilbert’s tenth problem 00:05:00
2.E. The entscheidungsproblem, the Church-turing thesis, and the coding of Turing machines and problems 00:05:00
Module: 03
3.A. Infinity, hotel Hilbert, and countable and uncountable sets 00:05:00
3.B. Decidable problems, the Halting Problem and its undecidability, and Universal Turing Machines 00:05:00
Module: 04
4.A. Reductions and direct reduction 00:05:00
4.B. Computable functions and mapping reduction 00:05:00
4.C. Rice’s Theorem and reductions via computation histories 00:05:00
5. Self-reproduction 00:05:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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