Alice, Bob, Mary and Jack are the users of a computer system. The files on the system can be broken down to the following categories:

Public Data, Sensitive Data, Admin files, Private data

where private data is the personal files of each of the users. The possible access rights to these file types are:

Given the following system usage requirements:

a$.$ Construct an active matrix to reflect these requirements.

User$/$Files Public Data Sensitive Data Admin files Private data

Bob R NA NA O

Alice O A NA O

Jack O O O O

Mary E O NA O

b$.$ Decompose the active matrix into an Access Control List $($ACL$)$ for each file type and capability tickets for each user.