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Title: Reachability problems in quaternion matrix and rotation semigroups
Authors: Bell, Paul C.
Potapov, Igor
Issue Date: 2008
Publisher: © Elsevier
Citation: BELL, P.C. and POTAPOV, I., 2008. Reachability problems in quaternion matrix and rotation semigroups. Information and Computation, 206 (11), pp.1353-1361.
Abstract: We examine computational problems on quaternion matrix and ro- tation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for ma- trix semigroups are undecidable in dimension two. The geometric interpretation of matrix problems over quaternions is presented in terms of rotation problems for the 2 and 3-sphere. In particular, we show that the reachability of the ro- tation problem is undecidable on the 3-sphere and other rotation problems can be formulated as matrix problems over complex and hypercomplex numbers.
Description: This is the author’s version of a work that was accepted for publication in the journal Information and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at: http://www.sciencedirect.com/science/article/pii/S0890540108000771
Version: Accepted for publication
DOI: 10.1016/j.ic.2008.06.004
URI: https://dspace.lboro.ac.uk/2134/12044
Publisher Link: http://dx.doi.org/10.1016/j.ic.2008.06.004
ISSN: 0890-5401
Appears in Collections:Published Articles (Computer Science)

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