Information Technology Reference
In-Depth Information
Ta b l e 7 . 1 3
A 4-node complete graph expressed in XML format
<
graph
>
<
node
#1
>
<
edges
>
2, 3, 4
</
edges
>
</
node
>
<
node
#2
>
<
edges
>
1, 3, 4
</
edges
>
</
node
>
<
node
#3
>
<
edges
>
1, 2, 4
</
edges
>
</
node
>
<
node
#4
>
<
edges
>
1, 2, 3
</
edges
>
</
node
>
</
graph
>
symbols have an implicit priority, therefore some dots can be avoided (for example,
multiplication and division are applied before sum and subtraction).
Dotted notation can be generalized as an alternative device with respect to paren-
theses (or used jointly with them). In general, dots can be used for breaking a
sequence into pieces. Firstly, the pieces without dots are aggregated, then pieces
between one dot are aggregated, and so on. In other words, dots indicate the order
of aggregation of components in a sequence. This provides a linear representation
of hypermultisets, with dots, that is, extra symbols which can be iterated any num-
ber of times. For example, the sequence below is the dot representation of mem-
brane/parenthesis structure:
(((
a
,
c
)(
a
,
c
)(
a
,
c
))
,
(
c
,
c
)
,
((
a
,
a
,
b
)(
a
,
a
,
b
)(
a
,
a
,
b
)))
.
(
ac
•
ac
•
ac
••
cc
••
aab
•
aab
•
aab
)
.
In the expression below:
(
3
+
5
)
×
((
12
×
10
)+(
7
×
13
))
parentheses are removed by putting near to the operation symbols a number of dots
representing their application priority (fewer dots for greater priorities). Its dotted
representation is the following:
3
+
5
ו•
12
×
10
+
•
7
×
13
.
