Reachability problems in quaternion matrix and rotation semigroups

Reachability Problems in Quaternion Matrix and Rotation Semigroups

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...

Computational problems in matrix semigroups

This thesis deals with computational problems that are defined on matrix semigroups, which play a pivotal role in Mathematics and Computer Science in such areas as control theory, dynamical systems, hybrid systems, computational geometry and both classical and quantum computing to name but a few. Properties that researchers wish to study in such fields often turn out to be questions regarding t...

Mortality in Matrix Semigroups

We present a new shorter and simplified proof for the undecidability of the mortality problem in matrix semigroups, originally proved by Paterson in 1970. We use the clever coding technique introduced by Paterson to achieve also a new result, the undecidability of the vanishing (left) upper corner. Since our proof for the undecidability of the mortality problem uses only 8 matrices, a new bound...

Examples of Undecidable Problems for 2-Generator Matrix Semigroups

Function spaces of Rees matrix semigroups

We characterize function spaces of Rees matrixsemigroups. Then we study these spaces by using the topologicaltensor product technique.