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Library for Boolean Functions in Algebraic Normal Form
Vasilišin, Maroš ; Mrázek, Vojtěch (referee) ; Dobai, Roland (advisor)
This bachelor thesis focuses on design and implementation of library in C language for manipulation od Boolean functions in Algebraic Normal Form. Majority of existing libraries for representation of Boolean functions is based on binary decision diagrams. Algebraic Normal Form presents several advantages over binary decision diagrams, for example Boolean value of function can be determined in linear time. Implemented library uses simple structures to effectively represent Boolean function in program. After experiments we determined that representation in Algebraic Normal Form has its applications, and in some cases it provides better results than representation in binary decision diagrams.
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Problem Encoding Methods in Evolutionary Design of Combinational Circuits
Sedláček, Adam ; Vašíček, Zdeněk (referee) ; Sekanina, Lukáš (advisor)
The thesis compares two different approaches to combinational circuit encoding for automated circuit design which uses evolutionary algorithms. The comparison was made between cartesian genetic programming and circuit represented in the algebraic normal form. Both methods were evaluated on a chosen set of circuits. The first test case criterion was the convergence of each particular method. The second optimization criterion was the area used on a chip. For accelerating the evaluation of fitness a parallel simulation was used. Implementation is in programming language C++ with Boost library. The pros and cons of both methods are summarised at the end of this work.
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Problem Encoding Methods in Evolutionary Design of Combinational Circuits
Sedláček, Adam ; Vašíček, Zdeněk (referee) ; Sekanina, Lukáš (advisor)
The thesis compares two different approaches to combinational circuit encoding for automated circuit design which uses evolutionary algorithms. The comparison was made between cartesian genetic programming and circuit represented in the algebraic normal form. Both methods were evaluated on a chosen set of circuits. The first test case criterion was the convergence of each particular method. The second optimization criterion was the area used on a chip. For accelerating the evaluation of fitness a parallel simulation was used. Implementation is in programming language C++ with Boost library. The pros and cons of both methods are summarised at the end of this work.
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On a matrix approach for constructing quadratic almost perfect nonlinear functions
Rezková, Zuzana ; Göloglu, Faruk (advisor) ; Žemlička, Jan (referee)
Search for new APN functions is an important topic in symmetric cryptography. The matrix approach for constructing quadratic APN functions was described by Y. Yu, M. Wang and Y. Li in 2014. The approach takes advantage of the one to one correspondence between quadratic homogenous APN functions and quadratic APN matrices. The aim of this thesis is to explain the matrices used in the original paper and show that similar matrices can be constructed directly from the algebraic normal form of the APN function. In Chapter 2 we introduce the original method adding extra theorems and expanding the proofs for better understanding. In Chapter 3 we define the matrices obtained simply from the algebraic normal form. In Chapter 4 we give examples of the matrices for chosen APN functions and show how they are related. 1
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Library for Boolean Functions in Algebraic Normal Form
Vasilišin, Maroš ; Mrázek, Vojtěch (referee) ; Dobai, Roland (advisor)
This bachelor thesis focuses on design and implementation of library in C language for manipulation od Boolean functions in Algebraic Normal Form. Majority of existing libraries for representation of Boolean functions is based on binary decision diagrams. Algebraic Normal Form presents several advantages over binary decision diagrams, for example Boolean value of function can be determined in linear time. Implemented library uses simple structures to effectively represent Boolean function in program. After experiments we determined that representation in Algebraic Normal Form has its applications, and in some cases it provides better results than representation in binary decision diagrams.
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