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Topics of Bachelor SFE valid for the SFE held from summer semester of the academic year 2017/2018

The exam based on SFE topics consists from two questions, one is based on SFE topics from compulsory courses of the degree study programme and the second one is based on SFE topics from the branch of study.

The question shall start with a copy of the topics as can be seen here. The question can be extended or clarified by the committee for the SFE.

Column Subject refers to the main subject of the topic, but the topic can also be found in other subjects.

Topics from the branch of study

Topics from compulsory courses

# Label Topic Subject
1.BIE-SPOL-1 Chomsky hierarchy of formal languages and grammars. Turing machines, universal Turing machine, recursive-enumerable and recursive languages. The P, NP, and NP-complete classes of problems. BIE-AAG
2.BIE-SPOL-2 Regular languages: Deterministic and nondeterministic finite automata. Determinization of a finite automaton. Minimization of a deterministic finite automaton. Operations on finite automata. Regular grammars, expressions, and equations. BIE-AAG
3.BIE-SPOL-3 Context-free languages, context-free grammars, pushdown automata and its variants. Models of parsing of context-free languages. BIE-AAG
4.BIE-SPOL-4 Basic notions of graph theory. Graph algorithms: breadth-first search and depth-first search, connected components, topological sort, distances in graphs, algorithms for minimum spanning tree construction and shortest paths in edge-weighted graphs. BIE-AG1
5.BIE-SPOL-5 Binary heaps, binomial heaps. Search trees and their balancing. Hash tables. BIE-AG1
6.BIE-SPOL-6 Asymmetric cryptosystems (the RSA cipher, the Diffie-Hellman protocol, the RSA digital signature), hash functions (SHA-2, HMAC). BIE-BEZ
7.BIE-SPOL-7 Symmetric block and stream ciphers (AES, 3DES, RC4) – basic parameters, block cipher modes of operation (ECB, CBC, CFB, OFB, CTR, MAC), their basic description and vulnerabilities. BIE-BEZ
8.BIE-SPOL-8 Public key infrastructure, key distribution, digital signature. Certificates, certificate authorities. Cryptographically secure pseudorandom number generators. BIE-BEZ
9.BIE-SPOL-9 Relational database and relational algebra as a query language. The SQL language (SELECT, DDL, DML, DCL, TCL). Declaration of integrity constraints in DDL. BIE-DBS
10.BIE-SPOL-10 Trasactions and their properties - ACID. BIE-DBS
11.BIE-SPOL-11 3 layers of data abstraction in databases (conceptual, implementational, physical). Structures for storying data in relational databases for fast access (basic structures, special structures, indexes, etc.). BIE-DBS
12.BIE-SPOL-12 Systems of linear equations and their solvability, Rouché–Capelli-Frobenius theorem and related notions, characterization of a set of solutions, Gaussian elimination. BIE-LIN
13.BIE-SPOL-13 Matrices: matrix-matrix multiplication, regular matrices, inverse matrices and its calculation, matrix eigenvalues and their calculation, matrix diagonalisation. BIE-LIN
14.BIE-SPOL-14 Propositional logic: truth tables, disjunctive and conjunctive normal forms, universal system of logical connectives, logical consequence and its verification. BIE-MLO
15.BIE-SPOL-15 Predicate logic: language, interpretation, satisfaction of formulas, logical consequence and its verification, theories and models. BIE-MLO
16.BIE-SPOL-16 Processes and threads, their implementation. Synchronization tools. Classical synchronization problems. Thread scheduling. Allocation of resources, Coffman's conditions, ways to resolve a deadlock. BIE-OSY
17.BIE-SPOL-17 Principles of translation of logical-to-physical addresses for the virtual paged memory with/without segmentation. Page replacement algorithms in virtual paged memory. BIE-OSY
18.BIE-SPOL-18 Data types in programming languages. Statically and dynamically allocated variables, linked lists. Modular programming, procedures and functions, input and output parameters. Compiler, linker, debugger. BIE-PA1
19.BIE-SPOL-19 Time and space complexities of algorithms. Searching algorithms (linear, binary), merging and sorting algorithms (BubbleSort, SelectSort, InsertSort, MergeSort, QuickSort). Lower bound of the sorting problem in the comparison model. Linear-time sorting algorithms. BIE-PA1
20.BIE-SPOL-20 Recursive decomposition of a problem to subproblems using the Divide-and-Conquer method. Recursion vs. iteration. Dynamic programming. BIE-PA1
21.BIE-SPOL-21 Object-oriented programming in C ++, encapsulation, inheritance, attributes, and methods, static attributes and methods, virtual methods, polymorphism, abstract classes, exceptions, templates, operator overloading, shallow and deep copy. BIE-PA2
22.BIE-SPOL-22 Abstract data types, specification and implementation. Stack, queue, array, list, table, and set. Implementation using linked structures, trees, and arrays. BIE-PA2
23.BIE-SPOL-23 ISO/OSI and TCP/IP network models. Link layer protocols. Forms of acknowledgement. Switching and routing. Principles of internetworking devices. BIE-PSI
24.BIE-SPOL-24 TCP/IP protocol family (IPv4, IPv6, TCP, UDP, application layer protocols). Data flow control. NAT - principle and usage. DNS system. BIE-PSI
25.BIE-SPOL-25 Rules for calculating probabilities, Bayes' formula. Random variables, common examples of distributons, cumulative distribution function, probability density function, moments. Independence of events and random variables. Central limit theorem, laws of large numbers. BIE-PST
26.BIE-SPOL-26 Basics of statistical inference, random samples, point estimates of the expectation and variance, interval estimates for the expectation, testing statistical hypotheses regarding the expectation. BIE-PST
27.BIE-SPOL-27 Combinational and sequential logic circuits (Mealy, Moore), their specification and implementation at the gate level. Logic function minimisation (using map representations). BIE-SAP
28.BIE-SPOL-28 Architecture of a digital computer, instruction cycle, basic types of the instruction set architectures (ISA). Computer memory subsystem, memory hierarchy, cache memory. BIE-SAP
29.BIE-SPOL-29 Representation of signed numbers and implementation of arithmetic operations (parallel adders/subtractors, arithmetic shifters, decoders, multiplexors, counters). Floating point number representations. BIE-SAP
30.BIE-SPOL-30 Tools supporting the software development process: bug tracking and task management tools (common tools, bug/task life cycle), source code management tools (principles of cooperation, main benefits, common tools). BIE-SI1.2
31.BIE-SPOL-31 Analytical domain class model, lifecycle of identified classes (goals, UML class diagram, UML state diagram). BIE-SI1.2
32.BIE-SPOL-32 Methods for solution of recurrent equations, formulation and solution of recurrent equations for time complexity analysis of algorithms. BIE-ZDM
33.BIE-SPOL-33 Modular arithmetics, introduction to number theory. Fermat's Little Theorem, diophantine equations, linear congruences, Chineese Remainder Theorem. BIE-ZDM
34.BIE-SPOL-34 Limit and derivative of a function (definition and properties, geometric interpretation), application to analysis of a graph of a function. BIE-ZMA
35.BIE-SPOL-35 Basics of integral calculus (primitive function, indefinite integral, Riemann integral (definition, properties, and geometric interpretation)). BIE-ZMA
36.BIE-SPOL-36 Numerical series (convergence, convergence tests, integral estimates of partial sums). BIE-ZMA
 
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