IA046 Computability

Faculty of Informatics
Spring 2008
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
prof. RNDr. Luboš Brim, CSc. (lecturer)
Guaranteed by
prof. RNDr. Mojmír Křetínský, CSc.
Department of Computer Science – Faculty of Informatics
Contact Person: prof. RNDr. Luboš Brim, CSc.
Timetable
Thu 14:00–15:50 B411
Prerequisites
Prerequisities: IB107 Computability and Complexity,MA006 Set Theory
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
there are 18 fields of study the course is directly associated with, display
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.
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.
  • Relativized 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
Assessment methods (in Czech)
Zkouška je písemná a ústní. V případě zadání průběžných testů během semestru, mají tyto podíl nejvýše 30% na závěrečném hodnocení. Pomocné materiály nejsou povoleny.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
Teacher's information
http://www.fi.muni.cz/usr/brim/IA046
The course is also listed under the following terms Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.
  • Enrolment Statistics (Spring 2008, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2008/IA046