Browsing Doctoral Dissertations by Title
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Knežević, Julka (Belgrade)[more][less]
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Timotijević, Marinko (Beograd , 2019)[more][less]
URI: http://hdl.handle.net/123456789/4818 Files in this item: 1
Disertacija_Marinko_Timotijevic.pdf ( 1.189Mb ) -
Vujošević Janičić, Milena (Beograd , 2013)[more][less]
Abstract: LAV is a system for statically verifying program assertions and locating bugs such as buffer overflows, pointer errors and division by zero. LAV is primarily aimed at analyzing programs written in the programming language C. Since LAV uses the popular LLVM intermediate code representation, it can also analyze programs written in other procedural languages. Also, the proposed approach can be used with any other similar intermediate low level code representation. System combines symbolic execution, SAT encoding of program’s control-flow, and elements of bounded model checking. LAV represents the program meaning using first-order logic (FOL) formulas and generates final verification conditions as FOL formulas. Each block of the code (blocks have no internal branchings and no loops) is represented by a FOL formula obtained through symbolic execution. Symbolic execution, however, is not performed between different blocks. Instead, relationships between blocks are modeled by propositional variables encoding transitions between blocks. LAV constructs formulas that encode block semantics once for each block. Then, it combines these formulas with propositional formulas encoding the transitions between the blocks. The resulting compound FOL formulas describe correctness and incorrectness conditions of individual instructions. These formulas are checked by an SMT solver which covers suitable combination of theories. Theories that can be used for modeling correctness conditions are: theory of linear arithmetic, theory of bit-vectors, theory of uninterpreted functions, and theory of arrays. Based on the results obtained from the solver, the analyzed command may be given the status safe (the command does not lead to an error), flawed (the command always leads to an error), unsafe (the command may lead to an error) or unreachable (the command will never be executed). If a command cannot be proved to be safe, LAV translates a potential counterexample from the solver into a program trace that exhibits this error. It also extracts the values of relevant program variables along this trace. The proposed system is implemented in the programming language Ñ++, as a publicly available and open source tool named LAV. LAV has support for several SMT solvers (Boolector, MathSAT, Yices, and Z3). Experimental evaluation on a corpus of C programs, which are designed to demonstrate areas of strengths and weaknesses of different verification techniques, suggests that LAV is competitive with related tools. Also, experimental results show a big advantage of the proposed system compared to symbolic execution applied to programs containing a big number of possible execution paths. The proposed approach allows determining status of commands in programs which are beyond the scope of analysis that can be done by symbolic execution tools. LAV is successfully applied in educational context where it was used for finding bugs in programs written by students at introductory programming course. This application showed that in these programs there is a large number of bugs that a verification tool can efficiently find. Experimental results on a corpus of students’ programs showed that LAV can find bugs that cannot be found by commonly used automated testing techniques. Also, it is shown that LAV can improve evaluation of students’s assignments: (i) by providing useful and helpful feedback to students, which is important in the learning process, and (ii) by improving automated grading process, which is especially important to teachers. URI: http://hdl.handle.net/123456789/4231 Files in this item: 1
phdVujosevicJanicicMilena.pdf ( 1.748Mb ) -
Marinković, Vesna (Beograd , 2015)[more][less]
Abstract: The problems of geometry constructions using ruler and compass are one of the oldest and most challenging problems in elementary mathematics. A solution of construction problem is not an illustration, but a procedure that, using given construction primitives, gives a “recipe” how to construct the object sought. The main problem in solving construction problems, both for a human and a computer, is a combinatorial explosion that occurs along the solving process, as well as a procedure of proving solutions correct. In this dissertation a method for automated solving of one class of construction problems, so-called location problems, is proposed. These are the problems in which the task is to construct a triangle if locations of three characteristic points are given. This method successfully proved most of the solvable problems from Wernick’s and Connelly’s list. For each of the problems it is checked if it is symmetric to some of the already solved problems, and then its status is determined: the problem can be found redundant, locus dependent, solvable, or not solvable using existing knowledge. Also, a description of the construction in natural-language form and in language GCLC is automatically generated, accompanied by a corresponding illustration, and correctness proof of the generated construction, followed by the list of conditions when the construction is correct. The proposed method is implemented within the tool ArgoTriCS. For proving generated constructions correct, the system ArgoTriCS uses a newly developed prover ArgoCLP, the automated theorem provers integrated within tools GCLC and OpenGeoProved, as well as the interactive theorem prover Isabelle. It is demonstrated that the proofs obtained can be machine verifiable. Within this dissertation, the system ArgoCLP (developed in collaboration with Sana Stojanovi´c) which is capable of automatically proving theorems in coherent logic is described. This prover is successfully applied to different axiomatic systems. It automatically generates proofs in natural-language form, as well as machineverifiable proofs, whose correctness can be checked using interactive theorem prover Isabelle. The important part of this system is a module for simplification of generated proofs whereby shorter and readable proofs are obtained. URI: http://hdl.handle.net/123456789/4406 Files in this item: 1
tezaVesnaMarinkovic.pdf ( 2.233Mb ) -
Tasković, Milan (Belgrade)[more][less]
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Pavlović-Lažetić, Gordana (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/45 Files in this item: 1
phdGordanaPavlovicLazetic.pdf ( 4.791Mb ) -
Ilić-Dajović, Milica (Belgrade , 1965)[more][less]
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Zekić, Mladen (Beograd , 2021)[more][less]
Abstract: Central place in this thesis occupy the coherence results for certain types of closed categories. Coherence results in category theory usually serve to provide a simple decision procedure for equality of arrows in some category. The approach to coherence that we follow here implies the existence of a faithfull functor from a freely generated category A of certain type to the category B in which an equality of arrows can be easily checked. Category B, which is of the same type as A, usually represents formalisation of some graphical language. Besides coherence, the second most important notion we consider in this thesis is the biproduct. The notion of biproduct in a category incorporates notions of coproduct and product. The main results in this thesis are coherence theorems for three types of closed categories with biproducts – symmetric monoidal closed categories with biproducts, com- pact closed categories with biproducts and dagger compact closed categories with dagger biproducts. Further, we present a new proof of the well-known Kelly-Mac Lane coherence theorem for symmetric monoidal closed categories. The methods we use in that proof are completely proof-theoretical, and one of the key elements in it is the cut-elimination theorem. In all the above coherence results, the graphical language is based on the category of one-dimensional cobordisms. Finaly, we give certain criteria for existence of biproducts in monoidal categories. In this regard, we rely on recent research that characterizes certain type of monoidal categories with finite biproducts by using the existence of right duals of some distinguished objects. Our criteria are a generalization of this result. URI: http://hdl.handle.net/123456789/5307 Files in this item: 1
mladen.zekic.disertacija.pdf ( 1.018Mb ) -
Leko, Marko (Beograd , 1980)[more][less]
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Leko, Marko (Belgrade , 1963)[more][less]
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Atanasijević, Ksenija (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/183 Files in this item: 1
phdKsenijaAtanasijevic.pdf ( 1.987Mb ) -
Arsenović, Mihajlo (Belgrade)[more][less]
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Pevac, Lazar (Belgrade)[more][less]
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Zeada, Samira (Belgrade , 2015)[more][less]
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Zeada, Samira (Beograd , 2015)[more][less]
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Ziada, Samira (Beograd , 2015)[more][less]
Abstract: This thesis has been written under the supervision of my mentor Prof. Aleksandar T. Lipkovski at the University of Belgrade in the academic year 2014- 2015. The topic of this thesis is Classi cation of Monomial Orders In Polynomial Rings and Gr obner Basis. The thesis is divided into four chapters let us review the content and the main contributions to this doctoral thesis. In the rst chapter (page. 1-6), the de nitions, features and examples of the notions basic for this thesis are given. Also, relevant properties of the multivariate polynomial ring and the division with reminder algorithm are recalled. In Chapter 2 (page. 7-22), the classi cation of monomial orderings for multivariate polynomial rings is displayed (given) in detail, with special emphasis on the case of two variables. The connection of this classi cation and the well known classi cation of Robiano is exposed in detail. It is an unusual and a little-known fact that the set of di erent monomial orderings with the natural topology is a Cantor set. Chapter 3 (page. 23-40) and Chapter 4 (page. 41-51) contain the main contributions of the thesis. In Chapter 3, the new approach to the analysis of the division with reminder algorithm is presented, based on set theoretic partial orderings (Section 3.3). Thus, the new evidence for (proof of ) Buchbergers result on niteness of the division procedure, regardless of a choice of the leading terms for the next dividing, is obtained. Likewise, in order to investigate Hilbert's original contribution and links with later considerations, we present his proof of the famous Hilbert basis theorem, on the basis of his original papers (section 3.5). In Chapter 4 (page. 41-51), a result from Chapter 3 is used for another new characterization of Gr obner basis, apparently weaker than well-known ones, to be obtained. Namely, it is shown that the bases G = ff1; : : : ; fkg of an ideal I is Gr obner if and only if, for any f from I, the support SuppG(f) is not empty. This condition is (only outwardly) weaker than a typical condition that the leading term of f belongs to SuppG(f). And describe the Gr obner fan of an ideal I and give an algorithm In a special case of two variables. URI: http://hdl.handle.net/123456789/4304 Files in this item: 1
phdSamiraZiada.pdf ( 465.6Kb ) -
Danić, Dimitrije (, 1885)[more][less]
Abstract: Tema Danićeve disertacije su konformna preslikavanja eliptičkog paraboloida na ravan, prateći definicije i formalizam koje je uveo Gaus (F. Gauss) za tu vrstu preslikavanja. U tom razmatranju izveo je određene parcijalne diferencijalne jednačine koje takođe analizira i rešava. Njegov doprinos bile su metode u rešavanju kompleksnih eliptičkih integrala, uvođenju eliptičkih transformacija i primeni eliptičkih funkcija u rešavanju ovih parcijalnih jednačina. URI: http://hdl.handle.net/123456789/4796 Files in this item: 3
DDanic_thesis_documentation.pdf ( 239.6Kb )DDanic_thesis_transl_SRB.pdf ( 1.764Mb )DDanic_thesis.pdf ( 1.420Mb ) -
Mijajlović, Žarko (Belgrade , 1977)[more][less]
Abstract: Part1. Basic notions of model theory are given. Part2. Dual notions in categories of Boolean algebras and Stone spaces are studied in respect to natural contra-variant functor. The cellularity number of a Boolean algebra B, celB is studied, certain cardinal properties are proved, e.g. it is consistent with ZFC that celB is attained for every Boolean algebra B. Part3. Lindenbaum algebras of first-order theories are studied in details. It is proved that every Boolean algebra is isomorphic to the Lindenbaum algebra B1 of Σ1 formulas of certain first-order complete theory. Stability number ST(k) of a first-order theory T is studied, and it is shown that ST(k) = Ku(k), where Ku(k) is the Kurepa number (Kurepa introduced it in 1935) and T is the theory of dense linear ordering without end-points, while the cardinality of the Stone space of B1(A), A is a model of T, is equal to ded(A), the Dedekind number of the ordering A. Ku(k)= sup{ded(A): A is a model of T, |A|=k}. Part4. Σn Πn ramifications of various notions in model theory are defined and studied, e.g. elementary embeddings, completeness, chains, direct limits, diagram properties, etc. Preservation theorems for these types of formulas are proved. Examples for including ordered structures and algebraic fields are given. Part5. Model completions and elimination of quantifiers are studied. As an application, it is proved that by means of model theory that the classes of Boolean algebras and distributive lattices with the least and the greatest elements are Jonsson’s classes. Algebraic description of saturated models of submodel-complete theories are given, unifying results of Haussdorff (dense linear ordering), Erdös, Gillman (ordered fields) and Boolean algebras (Negrepontis) for homogeneous-universal models. Part6. Here is studied what model-theoretic properties are absolute in ZF in the sense introduced by Levy, i.e. in which cases strong hypothesis (AC, GCH, V=L) can be eliminated from the proof of these properties. It is shown that the following properties of first-order theories are absolute: the consistency, completeness, model-completeness and elimination of quantifiers. These gives new light on model-theoretic proofs of these properties. URI: http://hdl.handle.net/123456789/196 Files in this item: 1
phdZarkoMijajlovic.pdf ( 27.39Mb ) -
Božić, Milan (Belgrade , 1983)[more][less]
Abstract: The thesis consists of five chapters. In the introductory chapter some relational-operational structures building of sets of formulas in calculi RA^+ and R^+ are presented. These structures are used in other chapters in making of the canonical frames of Kripke’ type for semantic of positive fragments of relevant propositional calculi. In Chapter 1, the semantic of these positive fragments, which is a mixture of known Routley & Meyer’s and Maksimova’s semantics, is presented. A new way for the semantic of negation in relevant logics is introduced in Chapter 2. It this way semantic completeness theorems for a large class of expansions of the logic R_min are proved. It is shown that Routley & Meyer’s semantic for the logic R is a special case of that semantic. Relevant modal logics are studied in Chapter 3. A semantic of Kripke’s type by which a completeness of a large class of modal logics whose basics are different relevant calculi with or without negation is introduced. A characterization of a large class modal i.e. Hintikka, schemas is given too. They contain almost all modal schemas characterized by formulas of the first order. Moreover, it is proved that the only known semantic for the calculus R_⊙ is a special case of the semantic given in this chapter. Semantics of relevant calculi which are not distributive are studied in Chapter 4. It is shown that semantics of non-distributive relevant logics radically change Kripke’s semantic. URI: http://hdl.handle.net/123456789/340 Files in this item: 1
phdMilanBozic.pdf ( 36.24Mb ) -
Tošić, Ratko (Belgrade , 1978)[more][less]
Abstract: The thesis consists of five chapters. In Chapter 1 definitions and well-known results from the theory of Boolean algebras and Boolean functions are given. In Chapter 2 of the thesis some properties of Boolean functions, which preserve constants under finite Boolean algebras, are presented by using the component representation. Their consequences about the number of Boolean’s functions are also given. The theorems which are the generalization of Scognmaiglio’s theorem and Andreoli’s theorem for Boolean functions with one variable, are proved in Chapter 3. The following new notions are introduced for monotone logical functions: the profile, the level, homogeneous, the corresponding matrix, etc. Some properties of these functions are shown and some consequences about the number of homogeneous monotone logical functions are presented. In Chapter 4 the applications of monotone Boolean functions in solving the problems of search theory (a branch of the theory of information) are presented. It is shown that the general problem of a type is, in fact, the problem of identifications of homogeneous monotone Boolean functions of the given profile by checking the value of that function for combinations of values of variables. Optimal or almost optimal solutions for some profiles are shown. It is also shown that monotonic logical functions are natural instrument for the generalization of these problems. Some open problems are presented in Chapter 5. URI: http://hdl.handle.net/123456789/356 Files in this item: 1
phdRatkoTosic.pdf ( 3.843Mb )