113 Прикладна математика

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https://ekmair.ukma.edu.ua/handle/123456789/18299
Освітня програма: "Прикладна математика"

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Browsing 113 Прикладна математика by Subject "bachelor thesis"

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    Binary relations between binary operations
    (2021) Bilyi, Illia; Козеренко, Сергій
    Let Bin(X) be a collection of all groupoids on some non-empty set X. De ne the operation : Bin2(X) ! Bin(X) so that x( )y = (x y) (y x) for all x; y 2 X and (X; ); (X; ) 2 Bin(X). Let lz denote left-zero operation (8x; y 2 X : x lz y = x) on X. Then, (X; lz) is an identity of (Bin(X); ). Similarly, de ne right-zero rz 2 Bin(X) (8x; y 2 X : x rz y = y). We consider the center of (Bin(X); ) and represent its elements as graphs. Furthermore, we investigate distributivity from the left in Bin(X) and its interaction with -product. We show that the only operation that is left- distributive over all possible 2 Bin(X) is rz 2 Bin(X) and that any 2 Bin(X) is left-distributive over lz; rz 2 Bin(X).
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    Boolean network optimization by stochastic rewiring
    (2024) Черевко, Крiстiна; Олійник, Богдана
    This bachelor thesis introduces novel algorithms for the area minimization of Multi-Input And-Inverter Graphs (MAIGs) within the field of logic synthesis. The primary focus is on the implementation of a new method named "Boolean network optimization by stochastic rewiring". This approach significantly diverges from traditional techniques like algebraic factoring and AIG rewriting by adopting a global strategy to add and remove wires at various locations within the circuit. The method relies on a simple randomization strategy to produce structural variations in the AIGs. Additionally, the thesis formulates and proves a new criterion for acceptable fanins, which ensures valid insertions and deletions without compromising the functionality of the circuit. Experimental results validate the effectiveness of the proposed algorithm in optimizing benchmark circuits. This work is important as it addresses the growing demand for smaller, more efficient circuits in modern electronics, potentially reducing manufacturing costs and enhancing performance.
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    Left-distributivity relation on the semigroup Bin(X)
    (2022) Krolevets, Mariia; Kozerenko, Serhiy
    Let X be a nonempty set. Bin(X) is the collection of all groupoids defined on X. Let ; 2 Bin(X). We define a binary operation on Bin(X) as follows: 8x; y 2 X : x[ ]y = (x y) (y x): In fact, (Bin(X); ) is a monoid with left-zero operation lz being its identity, where 8x; y 2 X : x lz y = x. ZBin(X) is the set of all elemets of Bin(X) that commute with every other elements under . In this thesis, we study the left-distributivity relation on the semigroup Bin(X) and the group ZBin(X).We research the question of trivial left-distributivity neighborhoods in Bin(X). Furthermore, we give a criterion, which characterizes those elements of ZBin(X), which the given element distributes from the left with.
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    LLM-based Smart Chatbot Design Using LangChain Framework
    (2024) Колодяжна, Дарія; Кузьменко, Дмитро
    This work presents the development of a smart chatbot called "Legislative Assistant" that assists Ukrainian lawyers and citizens in navigating legislative acts. The chatbot utilizes large language models (LLMs), specifically the Mistral-7B-Instruct-Ukrainian model, integrated with the LangChain framework and retrieval-augmented generation (RAG) techniques. By creating embeddings from a corpus of Ukrainian legislative acts and optimizing retrieval using RAG, the chatbot provides accurate and up-to-date responses to queries related to legislation. This work covers theoretical aspects such as the evolution of language models, transformer architectures like Mistral 7B and the concept of retrieval-augmented generation (RAG) for incorporating external data into language model responses.