  In this thesis, we use normal surface theory to understand certain properties
of minimal triangulations of compact orientable 3-manifolds. We describe the
collapsing process of normal 2-spheres and disks. Using some geometrical
constructions to take connected sums of triangulated 3-manifolds, we obtain the
following result: given a minimal triangulation of a closed orientable
3-manifold M, it takes polynomial time in the number of tetrahedra to check if
M is reducible or not.
