Rekurzivne multifunkcije

master's thesis

• Author: Elvir Baltić
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Committee member: Robert Manger (član povjerenstva)
• Committee member: Damir Bakić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U prvom poglavlju proučavaju se primitvno rekurzivne funkcije i njihova svojstva te se ujedno dokazuje rekurzivnost nekih poznatih uobičajenih funkcija. U drugom poglavlju uvodi se pojam rekurzivnih funkcija \(\mathbb{N}^k \to \mathbb{N}\) te se dokazuju neke činjenice vezane za te funkcije koje su potrebne u daljnjem dijelu rada. Nadalje, definira se pojam rekurzivnog skupa te se proučavaju neka svojstva takvih skupova. U trećem poglavlju proučavaju se funkcije oblika \(\mathbb{N}^k \to \mathcal{P}(\mathbb{N}^n)\). Za takve funkcije definira se kada su rekurzivne te kada su rekurzivno omeđene. Posebno, proučavaju se tzv. r.r.o. funkcije \(\mathbb{N}^k \to \mathcal{P}(\mathbb{N}^n)\). Navode se neki primjeri takvih funkcija te se dokazuju neki rezultati vezani za takve funkcije.

Abstract (english)

In first chapter we study primitive recursive functions and their properties. We also prove recursivity of some common examples of functions. In second chapter we introduce concept of recursive functions \(\mathbb{N}^k \to \mathbb{N}\) and we prove some facts related to these functions important for further work. In addition we define recursive sets and study their properties. In third chapter we study functions \(\mathbb{N}^k \to \mathcal{P}(\mathbb{N}^n)\). For these functions we define when they are recursive and when they are recursively bounded. Specially, we study so called r.r.b. functions \(\mathbb{N}^k \to \mathcal{P}(\mathbb{N}^n)\). We give examples of such functions and we proove some related results.

• Keywords: rekurzivna funkcija; primitivno rekurzivne funkcije; rekurzivni skup
• Keywords (english): recursive function; primitive recursive function; recursive set
• Language: croatian
• URN:NBN: urn:nbn:hr:217:088821
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-05-10 12:46:55