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This is a basic course on the theory of algorithms, computability and computational complexity. Roughly the first
half of the course is devoted to the introduction to computability theory: Turing machines. Computable functions.
Recursive and recursively enumerable languages and sets. Undecidable problems. The second half of the
course is devoted to the study of space and time complexity classes: Equivalence of PSPACE and NPSPACE.
Deterministic hierarchy theorems. Class NP. Polynomial reducibility among problems. Proofs of NP-
completeness. Approximation algorithms and approximation schemes.
Last update: T_KTI (28.04.2015)
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To teach basics of complexity theory and theory of computation. Last update: Kučera Petr, RNDr., Ph.D. (04.09.2014)
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To finish the subject it is necessary to get the credit and then to pass the exam. To get get the credit, it is necessary to acquire a given number of points for homework which are being solved during the semester. In case a student does not have enough points at the end of semester, it is possible to get some additional points for additional homework. Due to the nature of conditions for getting the credit it is not possible to have substitute dates of obtaining the credit. It is necessary to have the credit before coming to exam. Last update: Kučera Petr, RNDr., Ph.D. (18.09.2020)
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Lecture web pages (lecture presentation can be found there): http://ktiml.mff.cuni.cz/~kucerap/NTIN090/index-en.html
Sipser, M. Introduction to the Theory of Computation. Vol. 2. Boston: Thomson Course Technology, 2006.
Demuth O., Kryl R., Kučera A.: Teorie algoritmů I, II. SPN, 1984, 1989 (Only in Czech)
Soare R.I.: Recursively enumerable sets and degrees. Springer-Verlag, 1987
Odifreddi P.: Classical recursion theory, North-Holland, 1989
Garey, Johnson. Computers and intractability - a guide to the theory of NP-completeness, W.H. Freeman 1978
Arora S., Barak B.: Computational Complexity: A Modern Approach. Cambridge University Press 2009 (Draft available online). Last update: Töpfer Pavel, doc. RNDr., CSc. (25.05.2022)
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The exam has two parts, the written part and the oral part. The written part precedes the oral part and in case when a student fails to pass the written part, the exam does not continue with the oral part. In case the exam is finished due to failing the oral part, it is necessary to pass both the written part and the oral part at the next exam. Grade depends on the number of points given for both parts.
The written part consists of three assignments which correspond to the lecture syllabus. These assignments are similar to the exercises which are given during the practicals.
The requirements of the oral part correspond to the lecture syllabus to extent which was presented on the lecture during the semester. A list of possible questions is published at the web pages related to the subject before the exam period starts. Last update: Kučera Petr, RNDr., Ph.D. (08.10.2017)
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1) Turing machines and their variants, Church-Turing thesis. 2) Halting problem 3) RAM and their equivalence with Turing machines. Algorithmically computable functions. 4) Recursive and recursively enumerable languages and sets and their properties. 5) 1-reducibility and m-reducibility, 1-complete and m-complete sets. 6) Rice's theorem. 7) Nondeterministic Turing machines, basic complexity classes, classes P, NP, PSPACE, EXP. 8) Savitch's theorem - equivalence of PSPACE and NPSPACE. 9) Deterministic space and time hierarchy theorems. 10) Polynomial reducibility among problems. NP-hardness and NP-completeness. 11) Cook-Levin theorem, examples of NP-complete problems, proofs of NP-completeness. 12) Pseudopolynomial algorithms and strong NP-completeness. 13) Approximations of NP-hard optimization problems. Approximation algorithms and schemes. 14) Classes co-NP and #P. Last update: Töpfer Pavel, doc. RNDr., CSc. (14.01.2019)
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