Insight into the set of rights

The set of rights $R$ can be broken into two subsets : $R=R_C \cup R_F$ where $R_C$ is the set of capabilities and $R_F$ is the set of permissions that can be given to a file, for each possible uid. Let $U$ be the set of available uids plus a special element that will mean that the uid check is not needed. Let $C$ be the set of capabilities seen in section . Let $A=\{r,a,t,x\}$ be the set of file accesses.

We can write $R_C=U \times C$ and $R_F=U \times A \times F$. Thus an insight of $R$ could be the union of the two following tables where each row is an element of $R$. Let's have a very reduced disk with three files : $F=\{$/$,$/bin/$,$/bin/vi$\}$, and $U={-1,0,1000}$ (no uid test, id=root and first user).

-1	CAP_CHOWN
0	CAP_CHOWN
1000	CAP_CHOWN
-1	CAP_DAC_OVERRIDE
0	CAP_DAC_OVERRIDE
1000	CAP_DAC_OVERRIDE
...	...
-1	LIDS_OUTLAW
0	LIDS_OUTLAW
1000	LIDS_OUTLAW

-1	r	/
0	r	/
1000	r	/
-1	a	/
0	a	/
1000	a	/
-1	t	/
0	t	/
1000	t	/
-1	x	/
0	x	/
1000	x	/
-1	r	/bin/
0	r	/bin/
1000	r	/bin/
...	...	...
1000	x	/bin/vi