
Reconstruction of historical landscape features within manorial estates
Kučera, Petr ; Fialová, Zuzana
The methodology serves as a guideline for restoration of historical landscape features. The reason for using the methodology is a comparison of selected indicators of the condition of environment within the historical structure of manorial estates against the current state of landscape structure. The selection of relevant parameters focuses on the development of spatial and temporal development of landscape features that are in current terminology referred to as compositional parts of green infrastructure of an area. The importance of historical landscape elements in the structure of landscape lies in the support of ecosystem services that sustain the production capacity of landscape while enhancing environmental benefits.
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School on The Joy, Zdar nad Sázavou
Kučera, Petr ; Mačuda, Michal (referee) ; Vítek, Jiří (advisor)
The final bachelor's thesis responds to the request of the management of the Na Radosti school in Žďár nad Sázavou to design a new building for a democratic school. Due to the unsatisfactory current situation, where the school is located in several places in the town, it needs a new suitable space corresponding to their specific requirements and needs. A democratic school is a system of teaching based on the free choice of the individual. The new school, with a capacity of approximately 100 pupils, is to create a suitable space for learning, play and sport. Thanks to the designated land, it will also offer a connection to the landscape and create a creative and learning environment within it.

 

Konstrukce minimálních DNF reprezentací 2intervalových funkcí.
Dubovský, Jakub ; Čepek, Ondřej (advisor) ; Kučera, Petr (referee)
Title: A construction of minimum DNF representations of 2interval functions Author: Jakub Dubovský Department: Dep. of Theoretical Computer Science and Mathematical Logic Supervisor: doc.RNDr.Ondřej Čepek, Ph.D. Abstract: The thesis is devoted to interval boolean functions. It is focused on construction of their representation by disjunctive normal forms with minimum number of terms. Summary of known results in this field for 1interval functions is presented. It shows that method used to prove those results cannot be in general used for two or more interval functions. It tries to extend those results to 2interval functions. An optimization algorithm for special subclass of them is constructed. Exact error estimation for approximation algorithm is proven. A command line software for experimentation with interval function is part of the thesis. Keywords: boolean function, interval function, representation construction, ap proximation 1


Classes of Boolean Formulae with effectively soluable SAT.
Vlček, Václav ; Čepek, Ondřej (advisor) ; Kučera, Petr (referee)
This work studies classes of Boolean formulae with polynomially solvable satsiability problem (SAT). It investigates the behavior of these classes with respect to basic operation with formulae (variable and literal complementation, deletition of a literal or a clause, partial assignment and joining formulae). Furthermore the work studies recognition problems for a formula and a given class of functions, satisability testing, and mutual relations of the studied classes with respect to inclusion.


Properties of interval Boolean functions
Hušek, Radek ; Čepek, Ondřej (advisor) ; Kučera, Petr (referee)
Boolean function f is kinterval if  input vector viewed as nbit number  f is true for and only for inputs from given (at most) k intervals. Recognition of kinterval fuction given its DNF representation is coNPhard problem. This thesis shows that for DNFs from a given solvable class (class C of DNFs is solvable if we can for any DNF F ∈ C decide F ≡ 1 in polynomial time and C is closed under partial assignment) and fixed k we can decide whether F represents kinterval function in polynomial time. 1

 

Time complexity of Boolean minimization.
Gurský, Štefan ; Čepek, Ondřej (advisor) ; Kučera, Petr (referee)
This thesis deals with the time complexity of Boolean minimization  minimization of formulae that represent Boolean functions. It presents basic concepts from the area of Boolean functions, of their normal form representations and of minimization of these representations. A whole chapter is dedicated to Umans's [13] proofs of 2 completeness of minimization of general DNF formulae for both common measures of minimality. For a class of formulae called Matched this thesis presents new results that show that although satisfiability problem is easy for Matched formulae (difficult for an arbitrary formula), problems connected to minimization and minimization itself is as hard for Matched formulae as it is for general formulae.


Properties of kinterval Boolean functions
Gál, Pavol ; Čepek, Ondřej (advisor) ; Kučera, Petr (referee)
The main focus of this thesis is on interval Boolean functions. The thesis presents some fundamental knowledge about Boolean functions, their representations and, in particular, concentrates on positive boolean functions. The thesis quotes several known results about interval functions, such as their various properties, some recognition algorithms and their complexity. Then the thesis introduces commutative Boolean functions and studies the properties of commutative positive Boolean functions and some derived forms. The thesis formulates several propositions about their structure and number of intervals. The most important and new result is the algorithm for recognition of positive 3interval functions. Finally the thesis analyzes the structure and number of intervals of a few particular general Boolean functions.
