ERASMUS PROGRAMME
Academic Year 2014-2015
Incoming student mobility
Name of University Unit:
DEPARTMENT OF MATHEMATICS
COURSES OFFERED IN FOREIGN LANGUAGE
FOR ERASMUS INCOMING STUDENTS
Department or Chair
within the Faculty
Study program
Study level
Course title
Department of Mathematics
Second cycle study programme in mathematics
(Master level)
2nd cycle
Mathematical Theory of Computation
Course code
Language of instruction
English
Course objectives. Students will be introduced to basics
of mathematical theory of computation with emphasis
placed on regular languages, abstract models of
computation (Finite Automata and Turing Machines),
computability, decidability and basic classes of time and
space complexity.
Course description
Course prerequisites. Introduction to Set Theory,
Mathematical Logic, Combinatorial and Discrete
Mathematics
Syllabus.
Regular languages. Finite automata. Nondeterminism.
Regular expressions. Nonregular languages.
Context-free languages. Context-free grammars.
Pushdown automata. Non-context-free languages.
Church-Turing thesis. Turing machine. Variants of Turing
machines. The definition of algorithm.
Decidability. Decidable languages. The Halting problem.
Reducibility. Undecidable problems from language
theory. A simple undecidable problem. The recursion
theorem. Decidability of logical theories. Turing
reducibility.
Time complexity. Measuring complexity. The class P. The
class NP. NP-completeness. NP-complete problems. NPhard problems. Approximation Algorithms for NP-hard
combinatorial optimization problems.
Space complexity. Savitch’s theorem. The class PSPACE.
PSPACE-completeness. The classes L and NL. NLcompleteness. NL equals coNL.
Advanced topics in complexity theory. Randomized
computation. Interactive proof systems. Cryptography.
Quantum computation.
Form of teaching
Consultative teaching.
Form of assessment
The final exam which consists of a written and an oral part
is taken upon completion of lectures and exercises.
Acceptable results of mid-term exams taken by students
during the semester can replace the written part of the
final exam. Students can affect the final grade by doing
homework assignments or seminar papers during the
semester.
Number of ECTS
5
Class hours per week
2+2+0
Minimum number of
students
Period of realization
Winter semester
Lecturer
Dr. Zoran Tomljanović, Assistant Professor