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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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    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: 48
    Language of Content: Slovenian
    Mentor / Comentors:
    Name and SurnameIDFunction
    prof. dr. Borut Robič28Mentor
    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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