IA046 Computability

Faculty of Informatics
Spring 2022
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
Tue 15. 2. to Tue 10. 5. Tue 10:00–11:50 B411
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
there are 19 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.
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
The course is taught annually.
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 2021.

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
there are 19 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.
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.

IA046 Computability

Faculty of Informatics
Spring 2018
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
SOUHLAS
Prerequisities: IB107 Computability and Complexity,M4155
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 19 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.
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
English
Further Comments
The course is taught: every week.
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 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2016
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.
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Thu 16:00–17:50 B410
Prerequisites
Prerequisities: IB107 Computability and Complexity,M4155
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 19 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.
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 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 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2014
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.
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Thu 14:00–15:50 B410
Prerequisites
Prerequisities: IB107 Computability and Complexity,M4155
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.
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
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 2008, Spring 2010, Spring 2012, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2012
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.
Supplier department: Department of Computer Science – Faculty of Informatics
Timetable
Thu 12:00–13:50 D3
Prerequisites
Prerequisities: IB107 Computability and Complexity,M4155
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 19 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.
The main goals are: to understand basics of computability over real numbers; to learn additional results about classification of computational problems, in particular about arithmetical hierarchy; to get introduced into 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 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 2008, Spring 2010, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2010
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,M4155
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.
The main goals are: to understand basics of computability over real numbers; to learn additional results about classification of computational problems, in particular about arithmetical hierarchy; to get introduced into 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 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 2008, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

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.

IA046 Computability

Faculty of Informatics
Spring 2006
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 B410
Prerequisites
! I046 Computability II
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 7 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 annually.
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 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2005
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 B410
Prerequisites
! I046 Computability II
Prerequisities: IB107 Computability and Complexity,MA006 Set Theory
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 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 annually.
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 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2004
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
! I046 Computability II
Prerequisities: IB107 Computability and Complexity,MA006 Set Theory
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives (in Czech)
Předmět je zaměřen na hlubší studium výsledků teorie vyčíslitelnosti s důrazem na osvojení si používaných důkazových metod a technik.
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 annually.
Teacher's information
http://www.fi.muni.cz/usr/brim/IA046
The course is also listed under the following terms Autumn 2002, Spring 2005, Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Autumn 2002
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
Tue 12:00–13:50 B411
Prerequisites
! I046 Computability II
Prerequisities: IB107 Computability and Complexity,MA006 Set Theory
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Předmět je zaměřen na hlubší studium výsledků teorie vyčíslitelnosti s důrazem na osvojení si používaných důkazových metod a technik.
Syllabus
  • Recursion theorem, generalized Rice theorem, Rogers isomorphism theorem. Applications.
  • 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, applications to logic.
  • 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
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.fi.muni.cz/usr/brim/I046
The course is also listed under the following terms Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2023

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
there are 20 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.
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
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 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2019

The course is not taught in Spring 2019

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
SOUHLAS
Prerequisities: IB107 Computability and Complexity,M4155
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 19 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.
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
English
Further Comments
Course is no more offered.
The course is taught: every week.
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 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2017

The course is not taught in Spring 2017

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.
Supplier department: Department of Computer Science – Faculty of Informatics
Prerequisites
Prerequisities: IB107 Computability and Complexity,M4155
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 19 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.
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
The course is taught once in two years.
The course is taught: every week.
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 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2015

The course is not taught in Spring 2015

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.
Supplier department: Department of Computer Science – Faculty of Informatics
Prerequisites
Prerequisities: IB107 Computability and Complexity,M4155
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.
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
The course is taught once in two years.
The course is taught: every week.
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 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2013

The course is not taught in Spring 2013

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.
Supplier department: Department of Computer Science – Faculty of Informatics
Prerequisites
Prerequisities: IB107 Computability and Complexity,M4155
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.
The main goals are: to understand basics of computability over real numbers; to learn additional results about classification of computational problems, in particular about arithmetical hierarchy; to get introduced into 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
The course is taught once in two years.
The course is taught: every week.
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 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2011

The course is not taught in Spring 2011

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.
Prerequisites
Prerequisities: IB107 Computability and Complexity,M4155
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.
The main goals are: to understand basics of computability over real numbers; to learn additional results about classification of computational problems, in particular about arithmetical hierarchy; to get introduced into 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
The course is taught once in two years.
The course is taught: every week.
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 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2009

The course is not taught in Spring 2009

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.
Prerequisites
Prerequisities: IB107 Computability and Complexity,M4155
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.
The main goals are: to understand basics of computability over real numbers; to learn additional results about classification of computational problems, in particular about arithmetical hierarchy; to get introduced into relativized 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.
  • 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
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
The course is taught once in two years.
The course is taught: every week.
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 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.

IA046 Computability

Faculty of Informatics
Spring 2007

The course is not taught in Spring 2007

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.
Prerequisites
! I046 Computability II
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 6 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.
The course is taught: every week.
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 2008, Spring 2010, Spring 2012, Spring 2014, Spring 2016, Spring 2018, Spring 2021, Spring 2022.
  • Enrolment Statistics (recent)