Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

Sorted by: relevance · author · university · dateNew search

You searched for subject:(3X 1 problem). Showing records 1 – 2 of 2 total matches.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


University of Texas – Austin

1. -7002-7426. Challenging variants of the Collatz Conjecture.

Degree: MSin Computer Science, Computer science, 2018, University of Texas – Austin

The Collatz Conjecture (also known as the 3N + 1 problem) is simple to explain, yet proving that all positive integers following the Collatz Mapping must converge to 1 has eluded mathematicians for over half a century. Aaronson and Heule are exploring solving the Collatz Conjecture using an approach involving string rewrite systems: Aaronson transformed the Conjecture into a string rewrite system and Heule has been applying parallel SAT solvers on instances of this system. Similar approaches have been applied successfully to other mathematical problems. We started looking into simpler variants of the conjecture. This thesis defines some of these variants and investigates easily provable as well as very hard variants. We study the hardness of unsolved variants by computing the number of rewrite steps needed up to 1 billion. Our hardness prediction method suggests that proving termination of the challenging variants should be considerably easier compared to solving the original conjecture. Advisors/Committee Members: Aaronson, Scott (advisor), Heule, Marijn, 1979- (advisor).

Subjects/Keywords: Collatz Conjecture; 3X + 1 problem; String rewrite systems; SAT solving; Matrix interpretation

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

-7002-7426. (2018). Challenging variants of the Collatz Conjecture. (Masters Thesis). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/1559

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16th Edition):

-7002-7426. “Challenging variants of the Collatz Conjecture.” 2018. Masters Thesis, University of Texas – Austin. Accessed November 14, 2019. http://dx.doi.org/10.26153/tsw/1559.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7th Edition):

-7002-7426. “Challenging variants of the Collatz Conjecture.” 2018. Web. 14 Nov 2019.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-7002-7426. Challenging variants of the Collatz Conjecture. [Internet] [Masters thesis]. University of Texas – Austin; 2018. [cited 2019 Nov 14]. Available from: http://dx.doi.org/10.26153/tsw/1559.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-7002-7426. Challenging variants of the Collatz Conjecture. [Masters Thesis]. University of Texas – Austin; 2018. Available from: http://dx.doi.org/10.26153/tsw/1559

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete


University of Akron

2. Stroup, David A. Collatz’s Problem and Encoding Vectors.

Degree: MS, Mathematics, 2006, University of Akron

The first chapter introduces the Collatz conjecture. The second chapter presents a brief literature survey. The third chapter presents some theorems and conjectures regarding encoding vectors for various moduli. Appendices include a presentation of numerical data, which serves as a concrete illustration of the findings in chapter 3, and a Java program for independent analysis of the Collatz conjecture. Advisors/Committee Members: Norfolk, T. (Advisor).

Subjects/Keywords: Mathematics; Collatz conjecture; 3x+1 problem; Syracuse problem; Ulam Conjecture; hailstone numbers; Hasse algorithm

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Stroup, D. A. (2006). Collatz’s Problem and Encoding Vectors. (Masters Thesis). University of Akron. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=akron1145048595

Chicago Manual of Style (16th Edition):

Stroup, David A. “Collatz’s Problem and Encoding Vectors.” 2006. Masters Thesis, University of Akron. Accessed November 14, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=akron1145048595.

MLA Handbook (7th Edition):

Stroup, David A. “Collatz’s Problem and Encoding Vectors.” 2006. Web. 14 Nov 2019.

Vancouver:

Stroup DA. Collatz’s Problem and Encoding Vectors. [Internet] [Masters thesis]. University of Akron; 2006. [cited 2019 Nov 14]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1145048595.

Council of Science Editors:

Stroup DA. Collatz’s Problem and Encoding Vectors. [Masters Thesis]. University of Akron; 2006. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=akron1145048595

.