prikaz prve stranice dokumenta Mrežni automati
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master's thesis
Mrežni automati
Split: University of Split, University of Split, Faculty of science, 2019. urn:nbn:hr:166:600602
Botić, Mihaela
University of Split
Faculty of Science
Department of Mathematics

Institutional repository: Repository of Faculty of Science

Cite this document

Botić, M. (2019). Mrežni automati (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:600602

Botić, Mihaela. "Mrežni automati." Master's thesis, University of Split, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:166:600602

Botić, Mihaela. "Mrežni automati." Master's thesis, University of Split, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:166:600602

Botić, M. (2019). 'Mrežni automati', Master's thesis, University of Split, Faculty of Science, accessed 21 January 2025, https://urn.nsk.hr/urn:nbn:hr:166:600602

Botić M. Mrežni automati [Master's thesis]. Split: University of Split, Faculty of Science; 2019 [cited 2025 January 21] Available at: https://urn.nsk.hr/urn:nbn:hr:166:600602

M. Botić, "Mrežni automati", Master's thesis, University of Split, Faculty of Science, Split, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:166:600602

Metadata
TitleMrežni automati
Title (english)Automata networks
AuthorMihaela Botić
MentorDamir Vukičević (mentor)
Committee memberDamir Vukičević (predsjednik povjerenstva)
Committee memberSnježana Braić (član povjerenstva)
Committee memberJelena Pleština (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2019-09-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu smo uveli osnovne pojmove vezane za mrežne automate te dokazali teoreme koji pokazuju snagu neuronskih mreža i staničnih automata. Posebno bitan je taj da postoji univerzalan stanični automat, te da za svaki stanični automat postoji neuronska mreža koja ga simulira. Pomoću Lyapunovljevih funkcionala smo dokazali teoreme u kojima su dane granice za duljinu prijelaza i duljinu ciklusa. Za simetrične neuronske mreže smo pokazali da poprimaju cikluse perioda 1 i najviše 2, za sekvencijalnu i sinkronu iteraciju redom, dok su za antisimetrične mreže duljine 2 i 4 za sekvencijalnu i sinkronu iteraciju redom. Na posljetku, dokazana su dva teorema koja osiguravaju da postoje neuronske mreže s eksponencijalnim duljinama prijelaza, i to konstruirajući takvu neuronsku mrežu.
Abstract (english)
In this master’s thesis we have introduced basic terms related to automata networks and proved theorems that show the power of neural networks and cellular automata. Especially important are the ones which show that there exists universal cellular automata and that for every cellular automata exists neural network which simulates it. Using Lyapunov functionals we have proved theorems where we give bounds for transient length and cycle length. For symmetrical neural networks we have proved that their cycle lengths are 1 for sequential, and 1 or 2 for synchronous iteration, while in case of antisymmetrical neural networks cycle lengths are 2 and 4, for sequential and synchronous iteration respectively. At the end, we have proved two theorems which insure that there exist neural networks with exponential transient length, constructing network with that property.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:600602
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching
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 students and staff of home institution
Terms of useLicence In copyright icon
Created on2020-06-05 12:27:37