456-0090/01 – Computability and Complexity (VAS)

Gurantor departmentDepartment of Computer ScienceCredits8
Subject guarantorprof. RNDr. Petr Jančar, CSc.Subject version guarantorprof. RNDr. Petr Jančar, CSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
YearSemestersummer
Study languageCzech
Year of introduction1996/1997Year of cancellation2010/2011
Intended for the facultiesFEIIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
JAN59 prof. RNDr. Petr Jančar, CSc.
SAW75 doc. Ing. Zdeněk Sawa, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

Teaching methods

Summary

The course introduces basic notions, results and methods of theory of algorithms, in particular of computability and complexity theories. First, general methods of the design of algorithms are reviewed, and the (time, space) complexity of concrete algorithms is analyzed; RAM (random access machine) serves as the underlying abstract computer model. Then the notion of complexity for problems is discussed, and complexity classes are introduced. Special attention is given to the classes PTIME and NPTIME; their importance (from both the theoretical and the practical viewpoint) is explained. Then the notion of algorithmic undecidability is clarified. The course is completed by a short illustration of approximation, probabilistic as well as parallel and distributed algorithms.

Compulsory literature:

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Uvod ke kursu. Slozitost algoritmu. Model RAM. Odhady slozitosti. Nejhorsí vs. prumerný pripad. Analyza vybranych algoritmu. Metoda `rozdel a panuj'. Analyza dalsich algoritmu. `Greedy' algoritmy. Metoda dynamickeho programovani. Problemy, tridy slozitosti problemu, horni a dolní odhady. Turinguv stroj. Turingovy stroje a dalsi vypocetni modely; jejich vzajemna `polynomialni' simulace. Trida P (=PTIME) jako aproximace tridy prakticky zvladnutelných problemu. Trida NP (=NPTIME). Polynomialni preveditelnost. NP-uplnost. NP-uplne problemy. Otevrena otazka, zda P=NP. Dalsi tridy casove i prostorove slozitosti a jejich vzajemne vztahy. Dokazatelne nezvladnutelne problemy. Church-Turingova teze. Rozhodnutelnost a castecna rozhodnutelnost problemu. Univerzalni Turinguv stroj. Rekurzivni a rekurzivne spocetne mnoziny (jazyky). Rekurzivni a castecne rekurzivni funkce. Metoda diagonalizace. Nerozhodnutelnost problemu zastaveni. Dalsi nerozhodnutelne problemy. Riceova věta. Dalsi temata teorie algoritmu.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2008/2009 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 4 Compulsory study plan
2007/2008 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 4 Compulsory study plan
2007/2008 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2007/2008 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2007/2008 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2007/2008 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 4 Compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 4 Compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 4 Compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 4 Compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (B2612) Electrical Engineering and Computer Science (1801R001) Computer Science P Czech Ostrava 4 Compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 3 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 3 Compulsory study plan
2000/2001 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 3 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner