Question

14.4 The RC 4000 system, among others, has defined a tree of processes (called a process tree) such that all the descendants of a process can be given resources (objects) and access rights by their ancestors only. Thus, a descendant can never have the ability to do anything that its ancestors cannot do. The root of the tree is the operating system, which has the ability to do anything. Assume that the set of access rights is represented by an access matrix, A. A(x,y) defines the access rights of process x to object y. If x is a descendant of z, what is the relationship between A(x,y) and A(z,y) for an arbitrary object y?

Answer 1

A(x, y) defines the access rights of process x to object y.

x is a descendant of z.

Therefore, for any arbitrary object y, A(x, y) is a subset of A(z, y).

Process x is a descendant of process z. So, x is a subset of z.

Since x is a subset of z, for any arbitrary object y, A(x, y) is also a subset of A(z, y).