2019 Theory of Computation

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Instructor(s)
Tanaka Keisuke 
Course component(s)
Lecture
Day/Period(Room No.)
Tue3-4(W834)  Fri3-4(W834)  
Group
-
Course number
MCS.T323
Credits
2
Academic year
2019
Offered quarter
3Q
Syllabus updated
2019/4/2
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

This course gives students an introduction of the theory of computability, by extending knowledge of the theory of automata and language. This course mainly employs the model of the Turing machine. Students will learn the basic notion of computability on the Turing machine, which provides mathematical properties on the software and hardware of computers. The topics studied in this course include the Turing machine, the Church-Turing thesis, variations of the Turing machine, decidability, diagonal arguments, halting problems, reducibility, the Post correspondence problem, and the recursion theorem.

Student learning outcomes

By the end of this course, students will be able to understand:
1) notions of computability
2) the model of the Turing machine and its variations
3) techniques for the proofs of computability.

Keywords

Computation, Computability, the Turing machine, the Church-Turing thesis, variations of the Turing machine, decidability, diagonal arguments, halting problems, reducibility, the Post correspondence problem, the recursion theorem

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills

Class flow

The course consists of a standard lecture or practice exercise. A practice exercise includes supplementary materials and answers for the quizzes. Each class also includes quizzes on the contents of this class or previous classes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction, computation and computability, Turing machine I Understand the notion of the Turing machine
Class 2 Turing machine II, the Church-Turing thesis, variations of the Turing machine I Understand the content of the Church-Turing thesis
Class 3 Variations of the Turing machine II Understand the method on the proof for the equivalence on the variations
Class 4 Exercise-style lecture on the Turing machine and its variations Understand the properties of the variations of the Turing machine
Class 5 Decidability Understand the method for the proofs on decidability
Class 6 The diagonal arguments, the halting problem Understand the application of the diagonal arguments
Class 7 Reducibility Understand the notion of reducibility
Class 8 Exercise-style lecture on decidability and reducibility Understand the methods on reducibility
Class 9 Undecidability on language theory Understand the methods for the proofs
Class 10 The Post correspondence problem Understand the problem and its reducibility
Class 11 Mapping reducibility Understand the notion of mapping reducibility
Class 12 The recursion theorem Understand the argument of the proof
Class 13 Exercise-style lecture on mapping reducibility and the recursion theorem Understand the methods on mapping reducibility
Class 14 Introduction to the complexity theory Understand the basic notion of computational complexity
Class 15 Advanced topics Understand the advanced topics

Textbook(s)

Introduction to the Theory of Computation, Second Edition, Michael Sipser, Thomson Course Technology, 2005, ISBN 978-0534-95097-2.

Reference books, course materials, etc.

References will be announced in the first class.

Assessment criteria and methods

The evaluation consists of in-class quizzes (60%) and the final exam (40%).

Related courses

  • MCS.T213 : Introduction to Algorithms and Data Structures
  • MCS.T214 : Theory of Automata and Languages
  • MCS.T411 : Computational Complexity Theory
  • MCS.T405 : Theory of Algorithms
  • MCS.T508 : Theory of Cryptography

Prerequisites (i.e., required knowledge, skills, courses, etc.)

It is preferable to have the knowledge on the basics of algorithms and data structures and on the theory of automata and languages.

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