 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Computability

The course is not on the list Without time-table
Code Completion Credits Range Language
MI-VYC Z,ZK 4 2P+2C Czech
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Applied Mathematics
Synopsis:

Classical theory of recursive functions and effective computability,

with applications in provability theory.

Requirements:

Elementary arithmetics, a basic course in 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/
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2023-05-28
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