Izračunljivost realnih funkcija

master's thesis

• Title (english): Computability of real functions
• Author: Petra Staroverški
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Vedran Čačić (član povjerenstva)
• Committee member: Rudi Mrazović (član povjerenstva)
• Committee member: Goranka Nogo (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-09-22, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavali smo svojstva rekurzivnih funkcija. Tema je podijeljena na tri cjeline. U prvom poglavlju uveli smo pojmove inicijalnih i rekurzivnih funkcija te smo prikazali neka njihova osnovna svojstva. U drugom poglavlju definirali smo rekurzivne funkcije \(\mathbb{N}^k\rightarrow\mathbb{Z}\), \(\mathbb{N}^k\rightarrow\mathbb{Q}\) i \(\mathbb{N}^k\rightarrow\mathbb{R}\) te smo proučavali svojstva tih funkcija. Zatim smo uveli pojam izračunljivog broja i povukli analogiju s realnim rekurzivnim funkcijama. Treće poglavlje bavi se nizovno izračunljivim funkcijama, efektivnom uniformnom neprekidnošću te omeđenim i izračunljivim funkcijama.

Abstract (english)

In this master’s thesis we have studied properties of recursive functions. The topic is divided into three parts. In the first chapter, we have introduced the concepts of initial and recursive functions and presented some of their basic properties. In the second chapter, we defined the recursive functions \(\mathbb{N}^k\rightarrow\mathbb{Z}\), \(\mathbb{N}^k\rightarrow\mathbb{Q}\) and \(\mathbb{N}^k\rightarrow\mathbb{R}\)and studied their properties. Then we have introduced the notion of a computable number and drew an analogy with real recursive functions. The third chapter deals with sequentially computable functions, effective uniform continuity and bounded and computable functions.

• Keywords: rekurzivne funkcije; inicijalne funkcije; izračunljiv broj; nizovno izračunljive funkcije; efektivna uniformna neprekidnost
• Keywords (english): recursive functions; initial functions; computable number; sequentially computable functions; effective uniform continuity
• Language: croatian
• URN:NBN: urn:nbn:hr:217:622959
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-11-08 12:08:56