Chaitin's constant Omega - from definition to present

Metka Selak (2016) Chaitin's constant Omega - from definition to present. EngD thesis.

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Abstract

Problems, that led to the discovery of Chaitin's constant Ω are presented in this work. The constant Ω is the halting probability of the universal self-delimited Turing machine. Its definition is given. Its interesting features are presented, among which randomness and uncomputability are the most important. The constant Ω brings randomness and uncomputability to different areas of mathematics and computer science. This is a great problem for the traditional approach to problem solving. Three transformations of famous problems from different areas of mathematics, which relate bits of Ω to solutions to these problems, are given. Recent researches connected whit the constant Ω, mainly about computing its exact initial bits, are presented. A few examples of the halting probability in practise are listed. The presentation of Chaitin's constant Ω tries to be as intuitive as possible and still exact, while using only the necessary mathematics.

Item Type:

Thesis (EngD thesis)

Keywords:

Omega, Chaitin's constant, halting probability, halting problem, uncomputability, randomness, Turing machine

Number of Pages:

Language of Content:

Slovenian

Mentor / Comentors:

Name and Surname	ID	Function
prof. dr. Borut Robič	28	Mentor

Link to COBISS:

http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1537008579)

Institution:

University of Ljubljana

Department:

Faculty of Computer and Information Science

Item ID:

3363

Date Deposited:

20 Jun 2016 16:15

Last Modified:

30 Jun 2016 10:48

URI:

http://eprints.fri.uni-lj.si/id/eprint/3363

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