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University of Manchester

1. Fenner, Peter John. Some algorithmic problems in monoids of Boolean matrices.

Degree: 2018, University of Manchester

A Boolean matrix is a matrix with elements from the Boolean semiring ({0, 1}, +, x), where the addition and multiplication are as usual with the exception that 1 + 1 = 1. In this thesis we study eight classes of monoids whose elements are Boolean matrices. Green's relations are five equivalence relations and three pre-orders which are defined on an arbitrary monoid M and describe much of its structure. In the monoids we consider the equivalence relations are uninteresting - and in most cases completely trivial - but the pre-orders are not and play a vital part in understanding the structure of the monoids. Each of the three pre-orders in each of the eight classes of monoids can be viewed as a computational decision problem: given two elements of the monoid, are they related by the pre-order? The main focus of this thesis is determining the computational complexity of each of these twenty-four decision problems, which we successfully do for all but one. Advisors/Committee Members: JOHNSON, DR MARIANNE JOHNSON M, Kambites, Mark, Johnson, Dr Marianne johnson.

Subjects/Keywords: semigroup theory; computational complexity; Boolean matrices

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APA (6th Edition):

Fenner, P. J. (2018). Some algorithmic problems in monoids of Boolean matrices. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:315995

Chicago Manual of Style (16th Edition):

Fenner, Peter John. “Some algorithmic problems in monoids of Boolean matrices.” 2018. Doctoral Dissertation, University of Manchester. Accessed October 17, 2019. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:315995.

MLA Handbook (7th Edition):

Fenner, Peter John. “Some algorithmic problems in monoids of Boolean matrices.” 2018. Web. 17 Oct 2019.

Vancouver:

Fenner PJ. Some algorithmic problems in monoids of Boolean matrices. [Internet] [Doctoral dissertation]. University of Manchester; 2018. [cited 2019 Oct 17]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:315995.

Council of Science Editors:

Fenner PJ. Some algorithmic problems in monoids of Boolean matrices. [Doctoral Dissertation]. University of Manchester; 2018. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:315995

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