Reachability problems in quaternion matrix and rotation semigroups

Authors:
Paul Bell;Igor Potapov
Affiliations:
Department of Computer Science, University of Liverpool, Ashton Building, Ashton Street, Liverpool L69 3BX, UK;Department of Computer Science, University of Liverpool, Ashton Building, Ashton Street, Liverpool L69 3BX, UK
Venue:
Information and Computation
Year:
2008

Citing 8
Cited 2

Multiplicative equations over commuting matrices

Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Mathematics for 3D game programming and computer graphics

Mathematics for 3D game programming and computer graphics
Decision problems for semi-Thue systems with a few rules

Theoretical Computer Science - Insightful theory
Decidable and Undecidable Problems about Quantum Automata

SIAM Journal on Computing
On the membership of invertible diagonal and scalar matrices

Theoretical Computer Science
On undecidability bounds for matrix decision problems

Theoretical Computer Science
A Note on the Emptiness of Semigroup Intersections

Fundamenta Informaticae
Periodic and infinite traces in matrix semigroups

SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science

The Identity Correspondence Problem and Its Applications

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On the Computational Complexity of Matrix Semigroup Problems

Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju

Quantified Score

Hi-index	0.01

Visualization

Abstract

We examine computational problems on quaternion matrix and rotation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for matrix 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 rotation problem is undecidable on the 3-sphere and other rotation problems can be formulated as matrix problems over complex and hypercomplex numbers.