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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 TomljanoviÄ‡, Assistant Professor