Information Technology Reference
In-Depth Information
Table 3.
Protection state
∆
A
o
0
o
1
o
2
s
0
{r
1
,r
2
}
{r
0
,r
1
,r
2
}
{r
3
}
s
1
{r
0
,r
1
,r
2
}
{r
1
,r
2
}
∅
s
2
{r
1
,r
2
}
{r
1
,r
2
}
{r
0
,r
1
,r
2
}
-
“
if
C
1
and
...
and
C
i
then begin
π
1
;
...
;
π
j
end
”,
where
C
1
,
...
,
C
i
are elementary conditions like:
-
“
r
is in
A
(
σ, ω
)”,
and
π
1
,
...
,
π
j
are primitive operations. The number of elementary conditions
is
i
, a non-negative integer, and the number of primitive operations is
j
,apos-
itive integer. A HRU command is invoked by replacing all variables in it with
individuals of the appropriate types. After that, if the elementary conditions
C
1
,
...
,
C
i
are evaluated to true in terms of the current protection state then the
primitive operations
π
1
,
...
,
π
j
are executed. HRU commands will be denoted
by the letters
α
,
α
, etc, possibly with subscripts. By a HRU protection system,
we simply mean a finite set
of HRU commands. We shall say that
a command is conditional iff it contains at least 1 elementary condition. A HRU
protection system is monotonic iff none of its HRU commands contain a prim-
itive operation of the form “
destroy
”or“
delete
”. It is monoconditional iff none
of its HRU commands contain more that 1 elementary condition whereas it is
mono-operational iff none of its HRU commands contain more that 1 primitive
operation. HRU protection systems will be denoted by the letters
Π
,
Π
,etc,
possibly with subscripts. For all
i
{
α
1
,...,α
k
}
,let
C
HRU
(
i, j
) be the class of all HRU protection systems such that none of their
HRU commands contain more than
i
elementary condition or more than
j
prim-
itive operations and
∈{
0
,
1
,
2
,
∞}
and for all
j
∈{
1
,
2
,
∞}
+
HRU
(
i, j
) be the class of all monotonic HRU protection
C
systems in
C
HRU
(
i, j
). For example, the HRU protection system
Π
shown in
table 6 is in the class
+
HRU
(2
,
). Let
θ
be a substitution and
C
be an elemen-
tary condition. Suppose there is no variable in
θ
(
C
), i.e. every variable in
C
is
C
∞
Table 4.
Protection state
∆
A
o
0
o
1
o
2
s
0
{r
1
,r
2
}
{r
0
,r
1
,r
2
}
{r
3
}
s
1
{r
0
,r
1
,r
2
}
{r
1
,r
2
}
{r
4
}
s
2
{r
1
,r
2
}
{r
1
,r
2
}
{r
0
,r
1
,r
2
}
Table 5.
Protection state
∆
(4)
A
o
0
o
1
o
2
s
0
{r
1
,r
2
}
{r
0
,r
1
,r
2
}
{r
3
}
s
1
{r
0
,r
1
,r
2
}
{r
1
,r
2
}
{r
4
}
s
2
{r
1
,r
2
}
{r
1
,r
2
}
{r
0
,r
1
,r
2
,r
5
}
