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master's thesis
Izračunljivo prebrojivi skupovi
2023. urn:nbn:hr:166:506820
Šimunović, Nikola
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Šimunović, N. (2023). Izračunljivo prebrojivi skupovi (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:506820

Šimunović, Nikola. "Izračunljivo prebrojivi skupovi." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:506820

Šimunović, Nikola. "Izračunljivo prebrojivi skupovi." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:506820

Šimunović, N. (2023). 'Izračunljivo prebrojivi skupovi', Master's thesis, University of Split, Faculty of Science, accessed 26 December 2024, https://urn.nsk.hr/urn:nbn:hr:166:506820

Šimunović N. Izračunljivo prebrojivi skupovi [Master's thesis]. Split: University of Split, Faculty of Science; 2023 [cited 2024 December 26] Available at: https://urn.nsk.hr/urn:nbn:hr:166:506820

N. Šimunović, "Izračunljivo prebrojivi skupovi", Master's thesis, University of Split, Faculty of Science, Split, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:166:506820

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Metadata
TitleIzračunljivo prebrojivi skupovi
Title (english)Computably enumerable sets
AuthorNikola Šimunović
MentorMilica Klaričić Bakula (mentor)
Committee memberMilica Klaričić Bakula (predsjednik povjerenstva)
Committee memberJurica Perić (član povjerenstva)
Committee memberStipe Marić (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2023-06-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Obrađena je tema izračunljivo prebrojivih skupova. Izvedena je njihov konstrukcija preko definicije Turingovog stroja i izračunljive funkcije koristeći pritom Gödelovo numeriranje. Također, preko iste konstrukije su definirani česti matematički pojmovi kao što su izomorfizmi i permutacije, ali u kontekstu izračunljivosti. Potom su spomenute mnoge karakterizacije izračunljivo prebrojivih skupova kao i svojstva koja vežemo za njih. Jedna od najvažnijih karakterizacija je Teorem o nabrajanju (eng. Listing Theorem). Uveden je Teorem o rekurziji koji je temeljito obrađen u ovom radu. Za kraj je uveden pojam izračunljivo prebrojivih indeksa kao i svojstva koja vežemo za njih.
Abstract (english)
The aim of this thesis is to explain computable enumerable sets and their properties. Their construction was derived by defining a Turing machine and a computable function using Gödel numbering. Common mathematical concepts such as isomorphisms and permutations are also defined using the same construction, but in the context of computability. Subsequently, many characterizations of computable sets were mentioned, as well as the properties we associate with them. One of the most important characterizations is the Listing Theorem. The Recursion Theorem is introduced and discussed in detail in this thesis. Finally, the concept of computable countable indices is introduced, as well as the properties we associate with connecting them.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:506820
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to authenticated users
Terms of useLicence In copyright icon
Created on2023-06-21 10:19:16