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Simulation of the 8051 Microprocessor Architecture
Šimon, Petr ; Křoustek, Jakub (referee) ; Hruška, Tomáš (advisor)
More than 90% of processors are used in embedded systems today. Processor design for embedded systems is becoming complicated, so it should be automate as much as possible. This bachelor thesis deals with design of the microcontroller 8051. Design is created according to available documentation and ISAC language is used for model description. Results of model simulations are analyzed at the end of this thesis.
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ZX Spectrum Small Home Computer Emulator
Šimon, Petr ; Šimek, Václav (referee) ; Růžička, Richard (advisor)
Eight-bit computer ZX Spectrum has been created 30 years ago. It was extremely popular in its time and it has many fans till now, which still developing new application and games. There are also many new hardware extensions like IDE HDD driver, SD/MMC memory driver etc. The aim of this thesis is the design and develop of ZX Spectrum emulator, which will be based on modern PFGA technology and it will use modern periphery like VGA monitor, SD/MMC memory cards etc.
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Lebesgue density theorem for Haar measure
Sterzik, Marek ; Simon, Petr (advisor) ; Zahradník, Miloš (referee)
In this work, we study Lebesgue theorem analogy in the space 2k with Haar measure and a related theorem about -k-linkedness of the measure algebra of this space. The whole text is divided in three chapters. In the first chapter we explain some important definitions and basic properties of the measure space. The Lebesgue theorem is studied in the second chapter. After the essential definition of the point of density, the major part of the chapter is dedicated to the proof of the theorem. The theorem states, that the symmetric difference between any measurable set and the set of its points of density has measure zero. In the third chapter we study the -k-linkedness theorem; a theorem which states that the measure algebra of the space 2 is -k-linked, if 2 .
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Rabin-Miller test and the choice of a basis
Franců, Martin ; Simon, Petr (advisor) ; Čunát, Vladimír (referee)
This thesis is dedicated to various choices of basis in Rabin-Miller test. Short overview of similar methods is shown and some properties of structure of the set of strong liars are proved in theoretical part. Selected innovative choices of basis are tested on the set of odd composite numbers in range of 100 and 200 000 000 and the results are compared to results of tests with usual choices of bases. Hypothesis about possible improvement of test through using basis of special form with regard to tested number is proposed. Program used for compu- tations of these results is included. The program allows user to compare results of tests with various ways of choosing basis. The second part of the thesis contains documentation of the program.
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Connected compactifications
Vaváčková, Martina ; Simon, Petr (advisor) ; Vejnar, Benjamin (referee)
Title: Connected compactifications Author: Martina Vaváčková Department: Department of Theoretical Computer Science and Mathematical Logic Supervisor: prof. RNDr. Petr Simon, DrSc., Department of Theoretical Computer Science and Mathematical Logic Abstract: This thesis deals with connected compactifications of specific Tychonoff spaces. In particular, we are interested in the maximal elements with respect to the partial order over the set of all connected compactifications of a space. First we characterize maximal connected compactifications of spaces containing only finitely many components. We mention examples of spaces which have no connected compactification. Further we study connected compactifications of the rational numbers. We give a construction of a compactification analogical to the construction of the Čech-Stone compactification and we show a necessary and sufficient condition for its connectedness and maximality. Keywords: connected space, compact space, connectification, compactification
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Aplikace Baireovy věty
Peprníková, Ľubica ; Simon, Petr (advisor) ; Pyrih, Pavel (referee)
The aim of this work is to show, having three di®erent spaces and a set of elements with some common property in each one of them that the given set is the set of typical elements in that space. First we will show that a typical continuous function deffined on the interval [0; 1] is a nowhere differentiable one. Then we will show that a typical compact set in R2 is a discontinuum. And lastly, we will show that a typical planar continuum is an indecomposable one. A valuable tool will be the Baire theorem, the use of which will ensure, besides the density, also the fact that the given set is a countable intersection of open sets.
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Complete Boolean Algebras and Extremally Disconnected Compact Spaces
Starý, Jan ; Simon, Petr (advisor) ; Bukovský, Lev (referee) ; Thümmel, Egbert (referee)
We study the existence of special points in extremally disconnected compact topological spaces that witness their nonhomogeneity. Via Stone duality, we are looking for ultrafilters on complete Boolean algebras with special combinatorial properties. We introduce the notion of a coherent ultrafilter (coherent P-point, coherently selective). We show that generic existence of such ultrafilters on every complete ccc Boolean algebra of weight not exceeding the continuum is consistent with set theory, and that they witness the nonhomogeneity of the corresponding Stone spaces. We study the properties of the order-sequential property on σ-complete Boolean algebras and its relation to measure-theoretic properties. We ask whether the order-sequential topology can be compact in a nontrivial case, and partially answer the question in a special case of the Suslin algebra associated with a Suslin tree.
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