IA046 Computability

Faculty of Informatics
Spring 2021
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
Timetable
Wed 14:00–15:50 Virtuální místnost
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
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
Teacher's information
https://www.fi.muni.cz/usr/brim/home/#teaching
The course is also listed under the following terms Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2022.
  • Enrolment Statistics (Spring 2021, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2021/IA046