UINK118 Computability and Complexity Theory

Faculty of Philosophy and Science in Opava
Winter 2013
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. Ing. Petr Sosík, Dr. (lecturer)
RNDr. Miroslav Langer, Ph.D. (seminar tutor)
Guaranteed by
doc. Ing. Petr Sosík, Dr.
Institute of Computer Science – Faculty of Philosophy and Science in Opava
Prerequisites (in Czech)
UIAI019 Základy teoretické informatiky II || UIAI219 Základy teoretické informatiky II || UIBUC09 Theory of languages and automa || UINK106 Theory of languages and automa || UIN1006 Theory of Languages and Automa
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
Course objectives
Abstract machine models of computation - the Turing Machine and the RAM - are introduced. The concept of machine computability is built on their basis. The existence of non-computable problems is proven and their examples given. In the second part of the course, asymptotical time and space complexity of algorithms is introduced. This allows to describe the consumption of time and space of algorithms without fixing to any particular computing machine. Elementary complexity classes and their properties are studied, with special emphasis on the classes P and NP.
Syllabus
  • 1. Characterization of mechanical computing, the Turing - Church thesis.
    2. Turing Machine and its variants, universal Turing machine.
    3. Recursive and recursively enumerate sets, the diagonalization method.
    4. Decidable and undecidable problems, the reduction method.
    5. Rice Theorem, practical applications of the computability theory.
    6. Evaluation of time an space consumption of computer algorithms.
    7. Classes DTIME and DSPACE. Non-deterministic Turing machine, classes NTIME and NSPACE.
    8. The RAM machine and its computing power. Relations of the Turing Machine and RAM.
    9. Linear sped-up theorem and tape compression theorem, elementary complexity classes.
    10. Time and space hierarchy.
    11. Relations of time and space complexity classes.
    12. Reducibility and completeness, NP-complete problems.
    13. Complexity of probabilistic algorithms.
Literature
    recommended literature
  • Arora, S., Barak, B. Complexity Theory: A Modern Approach. Cambridge University Press, 2009. info
  • Kozen, D. Theory of Computation. Berlin: Springer-Verlag, 2006. info
  • Hopcroft, J. E., Motwani, R., Ullman, J. D. Introduction to Automata Theory, Languages and Computation. Upper Saddle River: Pearson Education Inc.,, 2003. info
  • Wiedermann, J. Teorie složitosti sekvenčních a paralelních výpočtů. Online studijní text. ÚI AV ČR, Praha, 2003. info
  • Sosík, P. Teorie vyčíslitelnosti. Online studijní text. Opava: FPF SU, 1996. info
  • Černá, I. Úvod do teórie zložitosti. Brno: FI MU, 1993. info
Assessment methods
Grade
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Course-credit:
- construction of a Turing machine due to an individual assignment
- at least 50% evaluation of written tests in the seminar classes
Exam:
- at least 50% evaluation of the written final test including the whole course topics
The course is also listed under the following terms Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022.
  • Enrolment Statistics (Winter 2013, recent)
  • Permalink: https://is.slu.cz/course/fpf/winter2013/UINK118