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Mathematical Institute Mathematical Institute Serbian Academy of Sciences and Arts, BelgradeSerbian Academy of Sciences and Arts, Belgrade

DEUKS Meeting DEUKS Meeting

Valencia, September 9-11, 2008, ValenciaValencia, September 9-11, 2008, Valencia

New PhD modules proposal

Zoran Ognjanović

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1.1. Promotion of the current European landscape of doctoral Promotion of the current European landscape of doctoral programmes in Serbia;programmes in Serbia;

2.2. Building-up and implementing pilot doctoral Building-up and implementing pilot doctoral programme according to the European innovative programme according to the European innovative recommendations;recommendations;

3.3. Introduction of improved and new teaching methods: Introduction of improved and new teaching methods: acquisition and exchange of knowledge in the specific acquisition and exchange of knowledge in the specific fields of teachers' and students‘ interests;fields of teachers' and students‘ interests;

4.4. Building-up the environment for linking the EHEA and ERA.Building-up the environment for linking the EHEA and ERA.

Specific objectives of the Specific objectives of the projectproject

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Possible contributionsPossible 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

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Groups related to CS and IT at Mathematical InstituteMathematical Institute

Cryptology Cryptology theory and applications theory and applications Logic in Computer Science and Logic in Computer Science and

Artificial Intelligence Artificial Intelligence Optimization and graph theory Optimization and graph theory Digitization of cultural and scientific Digitization of cultural and scientific

heritageheritage

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AimsAims

• To provide knowledge on To provide knowledge on formal formal methods in theoretical computer methods in theoretical computer sciencescience

• To obtain experiences on possible To obtain experiences on possible applicationsapplications

• To To allowallow involvement into research involvement into research projectsprojects

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PhD modules proposal

1.1. Fundamentals of cryptologyFundamentals of cryptology2.2. Selected topics of information securitySelected topics of information security3.3. ComputabilityComputability4.4. Automata and formal languagesAutomata and formal languages5.5. Computational complexityComputational complexity6.6. Knowledge representation and Knowledge representation and

automated deductionautomated deduction7.7. Categorial proof theory Categorial proof theory 8.8. Parallel programmingParallel programming9.9. Digitization of scientific and cultural Digitization of scientific and cultural

heritageheritage

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ComputabilityComputability

(Non)deterministic Turing Machines(Non)deterministic Turing Machines Partial recursive functionsPartial recursive functions Equality of different formal systemsEquality of different formal systems ChurchChurch’s thesis’s thesis DecidabilityDecidability Recursive sets and problemsRecursive sets and problems Recursively Recursively enumerableenumerable sets sets Halting problemHalting problem Abstract State MachinesAbstract State Machines Formal methods for specification and verificationFormal methods for specification and verification

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Automata and formal Automata and formal languageslanguages

Formal grammars and languagesFormal grammars and languages Finite automata and regular languagesFinite automata and regular languages Pushdown automata and context-free Pushdown automata and context-free

languageslanguages Applications in parsing of programming Applications in parsing of programming

languageslanguages Chomsky hierarchy Chomsky hierarchy Automata on infinite words and applications Automata on infinite words and applications

in verificationin verification

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Computational complexityComputational complexity

Turing Machines, (un)decidabilityTuring Machines, (un)decidability 0-notations0-notations Complexity classes, hierarchy, P-NPComplexity classes, hierarchy, P-NP Reduction and completenessReduction and completeness NP-complete problemsNP-complete problems Randomized computationRandomized computation Applications in cryptographyApplications in cryptography

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Knowledge representation and Knowledge representation and automated deductionautomated deduction

Classical logicClassical logic Description logics and semantic webDescription logics and semantic web Modal, temporal, intuitionistic, probability logicsModal, temporal, intuitionistic, probability logics Uncertain reasoningUncertain reasoning Non-monotonic reasoningNon-monotonic reasoning Automated deduction procedures Automated deduction procedures

(tableau,resolution, …)(tableau,resolution, …) Neural networksNeural networks

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Categorial proof theory Categorial proof theory

Syntactical categoriesSyntactical categories Monoidal categoriesMonoidal categories Symmetric monoidal categoriesSymmetric monoidal categories Bimonoidal categoriesBimonoidal categories Dissociative categoriesDissociative categories Bicartesian categoriesBicartesian categories Boolean categoriesBoolean categories Applications in computer scienceApplications in computer science

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Parallel programmingParallel programming

Models (Single Instruction Multiple Data, Multiple Models (Single Instruction Multiple Data, Multiple Instructions Multiple Data, shared memory, distributed Instructions Multiple Data, shared memory, distributed memory)memory)

Parallel programming paradigms Parallel programming paradigms

MPI (Message passing interface)MPI (Message passing interface)

Programming languagesProgramming languages

Examples of numerical and symbolic algorithmsExamples of numerical and symbolic algorithms

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Digitization of scientific andDigitization of scientific andcultural heritagecultural heritage

File formats (text, video, audio, images,...)File formats (text, video, audio, images,...) Standards for digitization and meta-dataStandards for digitization and meta-data CompressionCompression Protection of digitized dataProtection of digitized data Internet and digitization of heritageInternet and digitization of heritage Digital librariesDigital libraries Development of particular presentationsDevelopment of particular presentations

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List of possible lectureresList of possible lectureres

Miodrag MihaljeviMiodrag Mihaljevićć Žarko MijajlovićŽarko Mijajlović Zoran MarkovićZoran Marković Zoran OgnjanovićZoran Ognjanović Miodrag RaškovićMiodrag Rašković Kosta DošenKosta Došen Zoran PetrićZoran Petrić Predrag JaničićPredrag Janičić

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An example of research An example of research topicstopics

Probability logics:Probability logics:

allow strict reasoning about probabilities using allow strict reasoning about probabilities using well-defined syntax and semanticswell-defined syntax and semantics

formulas in these logics remain either true or formulas in these logics remain either true or false - do not have probabilistic (numerical) truth false - do not have probabilistic (numerical) truth valuesvalues

PP=s=s(A->B) (A->B) ٨٨ PP=t=t(A) -> P(A) -> P=r=r(B)(B) Kripke models with probability measures defined Kripke models with probability measures defined

over the worldsover the worlds

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Main problemsMain problems

Providing sound and complete axiom Providing sound and complete axiom systems systems

Compactness does not generally holdCompactness does not generally hold DecidabilityDecidability PSAT – SAT in probability logicPSAT – SAT in probability logic

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PSAT problem (1)PSAT problem (1)

PSAT in the simplest of the probability logics is PSAT in the simplest of the probability logics is NP-completeNP-complete

PSAT can be reduced to solving of a (huge) linear PSAT can be reduced to solving of a (huge) linear systemsystem

N propositional letters – 2N propositional letters – 2NN variables variables Standard linear system solving procedure is Standard linear system solving procedure is

unsuitable in practice unsuitable in practice Applications: uncertain reasoning, default Applications: uncertain reasoning, default

reasoning, reasoning, consistency of knowledge based systems, reliability checking, players’ beliefs in game theory and economics

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PSAT problem (2)PSAT problem (2)

Standard linear system solving procedure is Standard linear system solving procedure is unsuitable in practiceunsuitable in practice

Heuristic approach: genetic algorithms, variable Heuristic approach: genetic algorithms, variable neighborhood search (VNS), …neighborhood search (VNS), …

Developing parallel PSAT-checker combines 3 of Developing parallel PSAT-checker combines 3 of the proposed courses (the proposed courses (Computational complexity, Computational complexity, Knowledge representation and automated Knowledge representation and automated deductiondeduction, Parallel programming), Parallel programming)

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Thank you very much Thank you very much for your attentionfor your attention