FI:IA046 Computability - Course Information

IA046 Computability

The course is not taught in Spring 2023

Extent and Intensity

2/0/0. 2 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Luboš Brim, CSc. (lecturer)

Guaranteed by

prof. RNDr. Luboš Brim, CSc.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Computer Science – Faculty of Informatics

Prerequisites

Prerequisities: IB107 Computability and Complexity

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Applied Informatics (programme FI, N-AP)
• Information Technology Security (eng.) (programme FI, N-IN)
• Information Technology Security (programme FI, N-IN)
• Bioinformatics (programme FI, N-AP)
• Discrete algorithms and models (programme FI, N-TEI)
• Information Systems (programme FI, N-IN)
• Parallel and Distributed Systems (programme FI, N-IN)
• Computer Graphics (programme FI, N-IN)
• Computer Networks and Communication (programme FI, N-IN)
• Computer Systems (programme FI, N-IN)
• Embedded Systems (eng.) (programme FI, N-IN)
• Embedded Systems (programme FI, N-IN)
• Service Science, Management and Engineering (eng.) (programme FI, N-AP)
• Service Science, Management and Engineering (programme FI, N-AP)
• Social Informatics (programme FI, B-AP)
• Theoretical Informatics (programme FI, N-IN)
• Upper Secondary School Teacher Training in Informatics (programme FI, N-SS) (2)
• Artificial Intelligence and Natural Language Processing (programme FI, N-IN)
• Image Processing (programme FI, N-AP)

Course objectives

The course is focused on deeper understanding of results in the computability theory with emphasis on methods and techniques used to prove such results.
At the end of the course the students will be able to understand basics of computability over real numbers; will get acquainted with additional results about classification of computational problems, in particular about arithmetical hierarchy and relativised theory of computability.

Syllabus

• Recursion theorem, generalized Rice theorem, Rogers isomorphism theorem.
• Application to logic. Arithmetical sets and functions, Goedel-Rosser incompleteness theorem. Goedel's second incompleteness theorem.
• Relativised computability. Programs with oracles.
• Kleene hierarchy, Turing reducibility, tt-reducibility, arithmetical hierarchy.
• Post's problem.
• Analytical hierarchy.
• Computability on real numbers, complete partial orders, domains.

Literature

• Theory of Recursive Functions and Effective Computability. Edited by Hartley Rogers. Cambridge: Massachusetts Institute of Technology, 1987, 482 s. ISBN 0262680521. info

Teaching methods

lectures, homeworks

Assessment methods

Final exam is written. In the case homeworks are assigned, these are counted by maximum of 30% to the final evaluation. No reading materials are allowed during the final examination.

Language of instruction

Czech

Further Comments

Study Materials
The course is taught annually.
The course is taught: every week.

Teacher's information

https://www.fi.muni.cz/usr/brim/home/#teaching

• Enrolment Statistics (Spring 2023, recent)
  
• Permalink: https://is.muni.cz/course/fi/spring2023/IA046