I007 Computability

Faculty of Informatics
Spring 1999
Extent and Intensity
2/1. 3 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Luboš Brim, CSc. (lecturer)
Guaranteed by
Contact Person: prof. RNDr. Luboš Brim, CSc.
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
Syllabus
  • Algorithms, Church's thesis.
  • Syntax and semantics of WHILE-programs, computable functions, computability on words.
  • Standard enumeration of computable functions, enumeration (utm) theorem, parametrization (smn) theorem, effective numberings, Kleene's normal form theorem.
  • Recursive and recursively enumerable sets, enumeration of r.e. sets, closure properties.
  • Examples of undecidable problems, reduction and diagonalization, halting problem, verification problem, equivalence problem.
  • Riece's theorems.
  • Creative and productive sets, m-complete and 1-complete sets, effectively inseparable sets, simple and immune sets.
  • Recursion theorem, applications of the recursion theorem.
  • Alternative approaches to computability, recursive functions.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 1996, Spring 1997, Spring 1998, Spring 2000, Spring 2001, Spring 2002, Spring 2003.
  • Enrolment Statistics (Spring 1999, recent)
  • Permalink: https://is.muni.cz/course/fi/spring1999/I007