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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023

Computability

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Code Completion Credits Range Language
NI-VYC Z,ZK 4 2P+2C Czech
Lecturer:
Jan Starý (guarantor)
Tutor:
Jan Starý (guarantor)
Supervisor:
Department of Applied Mathematics
Synopsis:

Classical theory of recursive functions and effective computability.

Requirements:

Elementary arithmetics, a basic course in mathematical logic.

Syllabus of lectures:

1. Introduction. Elementary recursive functions.

2. Primitive recursive functions. Ackermann function.

3. General recursive functions. Universal functions.

4. Partial recursive functions.

5. Turing machines.

6. The power of Turing machines.

7. Universal machine. Halting Problem.

8. The equivalence of Turing machines and recursive functions.

9. Arithmetics: coding the language.

10. Recursive axiomatization.

11. (In)completeness and (un)decidability.

12. Diagonal lemma, Gödel's theorem.

Syllabus of tutorials:

1. Elementary recursive functions.

2. Primitive recursive functions

3. General recursive functions.

4. Partial recursive functions.

5. Turing machines.

6. Programming Turing machines.

7. Programming Turing machines.

8. Programming Turing machines.

9. Gödel coding and decoding.

10. Decidability: examples.

11. Undecidability: examples.

12. Diagonalization.

Study Objective:

The basic formalizations of an „algorithm“ and elementary questions of computability.

Study materials:

Church: An unsolvable problem of elementary number theory

Church: A note on the Entscheidungsproblem

Davis: Computability and unsolvability

Enderton: Elements of Recursion Theory

Kleene: Introduction to Metamathematics

Rogers: Theory of Recursive Functions and Effective Computability

Shoenfield: Mathematical Logic

Turing: On computable numbers

Černý: Výpočty I

Note:
Further information:
https://courses.fit.cvut.cz/NI-VYC/
Time-table for winter semester 2022/2023:
Time-table is not available yet
Time-table for summer semester 2022/2023:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
roomTH:A-1442
Starý J.
11:00–12:30
(lecture parallel1)
Thákurova 7 (FSv-budova A)
roomTH:A-1442
Starý J.
12:45–14:15
(lecture parallel1
parallel nr.101)

Thákurova 7 (FSv-budova A)
Tue
Wed
Thu
Fri
The course is a part of the following study plans:
Data valid to 2023-02-07
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