1. 1 Mathematical Institute Serbian Academy of Sciences and Arts, Belgrade DEUKS Meeting Valencia, September 9-11, 2008, Valencia New PhD modules proposal Zoran Ognjanović

2. 2 1. Promotion of the current European landscape of doctoral programmes in Serbia; 2. Building-up and implementing pilot doctoral programme according to the European innovative recommendations; 3. Introduction of improved and new teaching methods: acquisition and exchange of knowledge in the specific fields of teachers' and students‘ interests; 4. Building-up the environment for linking the EHEA and ERA. Specific objectives of the project

3. 3 Possible contributions to propose courses in different branches of CS and IT to offer a working environment for research activities to offer qualified experts and supervisors in some branches of CS and IT

4. 4 Mathematical Institute Groups related to CS and IT at Mathematical Institute Cryptology theory and applications Cryptology theory and applications Logic in Computer Science and Artificial Intelligence Logic in Computer Science and Artificial Intelligence Optimization and graph theory Optimization and graph theory Digitization of cultural and scientific heritage Digitization of cultural and scientific heritage

5. 5 Aims To provide knowledge on formal methods in theoretical computer science To provide knowledge on formal methods in theoretical computer science To obtain experiences on possible applications To obtain experiences on possible applications To allow involvement into research projects To allow involvement into research projects

6. 6 PhD modules proposal 1. Fundamentals of cryptology 2. Selected topics of information security 3. Computability 4. Automata and formal languages 5. Computational complexity 6. Knowledge representation and automated deduction 7. Categorial proof theory 8. Parallel programming 9. Digitization of scientific and cultural heritage

7. 7 Computability (Non)deterministic Turing Machines (Non)deterministic Turing Machines Partial recursive functions Partial recursive functions Equality of different formal systems Equality of different formal systems Church’s thesis Church’s thesis Decidability Decidability Recursive sets and problems Recursive sets and problems Recursively enumerable sets Recursively enumerable sets Halting problem Halting problem Abstract State Machines Abstract State Machines Formal methods for specification and verification Formal methods for specification and verification

8. 8 Automata and formal languages Formal grammars and languages Formal grammars and languages Finite automata and regular languages Finite automata and regular languages Pushdown automata and context-free languages Pushdown automata and context-free languages Applications in parsing of programming languages Applications in parsing of programming languages Chomsky hierarchy Chomsky hierarchy Automata on infinite words and applications in verification Automata on infinite words and applications in verification

9. 9 Computational complexity Turing Machines, (un)decidability Turing Machines, (un)decidability 0-notations 0-notations Complexity classes, hierarchy, P-NP Complexity classes, hierarchy, P-NP Reduction and completeness Reduction and completeness NP-complete problems NP-complete problems Randomized computation Randomized computation Applications in cryptography Applications in cryptography

10. 10 Knowledge representation and automated deduction Classical logic Classical logic Description logics and semantic web Description logics and semantic web Modal, temporal, intuitionistic, probability logics Modal, temporal, intuitionistic, probability logics Uncertain reasoning Uncertain reasoning Non-monotonic reasoning Non-monotonic reasoning Automated deduction procedures (tableau,resolution, …) Automated deduction procedures (tableau,resolution, …) Neural networks Neural networks

11. 11 Categorial proof theory Syntactical categories Syntactical categories Monoidal categories Monoidal categories Symmetric monoidal categories Symmetric monoidal categories Bimonoidal categories Bimonoidal categories Dissociative categories Dissociative categories Bicartesian categories Bicartesian categories Boolean categories Boolean categories Applications in computer science Applications in computer science

12. 12 Parallel programming Models (Single Instruction Multiple Data, Multiple Instructions Multiple Data, shared memory, distributed memory) Models (Single Instruction Multiple Data, Multiple Instructions Multiple Data, shared memory, distributed memory) Parallel programming paradigms Parallel programming paradigms MPI (Message passing interface) MPI (Message passing interface) Programming languages Programming languages Examples of numerical and symbolic algorithms Examples of numerical and symbolic algorithms

13. 13 Digitization of scientific and cultural heritage File formats (text, video, audio, images,...) File formats (text, video, audio, images,...) Standards for digitization and meta-data Standards for digitization and meta-data Compression Compression Protection of digitized data Protection of digitized data Internet and digitization of heritage Internet and digitization of heritage Digital libraries Digital libraries Development of particular presentations Development of particular presentations

14. 14 List of possible lectureres Miodrag Mihaljević Miodrag Mihaljević Žarko Mijajlović Žarko Mijajlović Zoran Marković Zoran Marković Zoran Ognjanović Zoran Ognjanović Miodrag Rašković Miodrag Rašković Kosta Došen Kosta Došen Zoran Petrić Zoran Petrić Predrag Janičić Predrag Janičić

15. 15 An example of research topics Probability logics: allow strict reasoning about probabilities using well- defined syntax and semantics allow strict reasoning about probabilities using well- defined syntax and semantics formulas in these logics remain either true or false - do not have probabilistic (numerical) truth values formulas in these logics remain either true or false - do not have probabilistic (numerical) truth values P =s (A->B) ٨ P =t (A) -> P =r (B) P =s (A->B) ٨ P =t (A) -> P =r (B) Kripke models with probability measures defined over the worlds Kripke models with probability measures defined over the worlds

16. 16 Main problems Providing sound and complete axiom systems Providing sound and complete axiom systems Compactness does not generally hold Compactness does not generally hold Decidability Decidability PSAT – SAT in probability logic PSAT – SAT in probability logic

17. 17 PSAT problem (1) PSAT in the simplest of the probability logics is NP- complete PSAT in the simplest of the probability logics is NP- complete PSAT can be reduced to solving of a (huge) linear system PSAT can be reduced to solving of a (huge) linear system N propositional letters – 2 N variables N propositional letters – 2 N variables Standard linear system solving procedure is unsuitable in practice Standard linear system solving procedure is unsuitable in practice Applications: uncertain reasoning, default reasoning, Applications: uncertain reasoning, default reasoning, consistency of knowledge based systems, reliability checking, players’ beliefs in game theory and economics

18. 18 PSAT problem (2) Standard linear system solving procedure is unsuitable in practice Standard linear system solving procedure is unsuitable in practice Heuristic approach: genetic algorithms, variable neighborhood search (VNS), … Heuristic approach: genetic algorithms, variable neighborhood search (VNS), … Developing parallel PSAT-checker combines 3 of the proposed courses (Computational complexity, Knowledge representation and automated deduction, Parallel programming) Developing parallel PSAT-checker combines 3 of the proposed courses (Computational complexity, Knowledge representation and automated deduction, Parallel programming)

19. 19 Thank you very much for your attention Thank you very much for your attention