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Course, academic year 2019/2020
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Structural Complexity - NTIN081
Title in English: Strukturální složitost
Guaranteed by: Department of Theoretical Computer Science and Mathematical Logic (32-KTIML)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: prof. Mgr. Michal Koucký, Ph.D.
Class: Informatika Mgr. - Teoretická informatika
Classification: Informatics > Theoretical Computer Science
Co-requisite : NTIN063
Annotation -
Last update: T_KTI (26.04.2016)
This course extends the basic course on computational complexity (NTIN063). It covers hierarchy theorems for probabilistic computation, time-space trade-offs for SAT, Toda's Theorem, pseudo-random generators and interactive protocols.
Aim of the course - Czech
Last update: T_KTI (26.04.2016)

Naučit další látku z teorie složitosti: vztahy mezi třídami složitosti, pseudonáhodné generátory a interaktivni protokoly.

Course completion requirements -
Last update: prof. Mgr. Michal Koucký, Ph.D. (10.06.2019)

Oral exam.

Literature -
Last update: T_KTI (26.04.2016)

Oded Goldreich, Computational Complexity: A Conceptual Perspective, Cambridge University Press 2008.

Sanjeev Arora, Boaz Barak. Complexity Theory: A Modern Approach. Cambridge University Press 2008.

D. van Melkebeek and K. Pervyshev. A Generic Time Hierarchy for Semantic Models With One Bit of Advice. Computational Complexity, 16: 139-179, 2007.

D. van Melkebeek. Time-Space Lower Bounds for Satisfiability. Bulletin of EATCS, 73: 57-77, 2001.

Requirements to the exam -
Last update: prof. Mgr. Michal Koucký, Ph.D. (10.06.2019)

The exam is oral from the material covered by the lectures. Each student gets reasonable time (at most three hours) for preparation upon receiving the questions.

Study materials (lecture notes, text books, etc.), computers and other electronic devices are not allowed during the exam.

Syllabus -
Last update: T_KTI (26.04.2016)

Nondeterministic time hierarchy and hierarchy for probabilistic computation

BPP and polynomial hierarchy

Time-space trade-off for SAT

Isolation Lemma and Toda's Theorem

Pseudo-random generators, Nisan's pseudo-random generator

Interactive protocols - Arthur-Merlin games (class AM, IP=PSPACE)

Multi-prover interactive protocols (MIP=NEXP)

 
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