All Outputs (3)

Reachability problems in quaternion matrix and rotation semigroups (2008)
Journal Article
Bell, P. (2008). Reachability problems in quaternion matrix and rotation semigroups. Information and Computation, 1353 - 1361. https://doi.org/10.1016/j.ic.2008.06.004

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 undeci... Read More about Reachability problems in quaternion matrix and rotation semigroups.

MATRIX EQUATIONS AND HILBERT'S TENTH PROBLEM (2008)
Journal Article
Bell, P. (2008). MATRIX EQUATIONS AND HILBERT'S TENTH PROBLEM. International Journal of Algebra and Computation, 1231 - 1241. https://doi.org/10.1142/S0218196708004925

We show a reduction of Hilbert's tenth problem to the solvability of the matrix equation over non-commuting integral matrices, where Z is the zero matrix, thus proving that the solvability of the equation is undecidable. This is in contrast to the ca... Read More about MATRIX EQUATIONS AND HILBERT'S TENTH PROBLEM.

On undecidability bounds for matrix decision problems (2008)
Journal Article
Bell, P. (2008). On undecidability bounds for matrix decision problems. Theoretical Computer Science, 3 - 13. https://doi.org/10.1016/j.tcs.2007.10.025

In this paper we consider several reachability problems such as vector reachability, membership in matrix semigroups and reachability problems in piecewise linear maps. Since all of these questions are undecidable in general, we work on lowering the... Read More about On undecidability bounds for matrix decision problems.