program dependence graph

1. Program dependence graph
 PDG can be expressed as G (N, E), N={n ∈ N | n means
that one of the statement in the program}, E={( m, n)|m, n ∈ N
Whether statement m implementation depends on the true and
false statement n, or exist variable V which is defined by m and
referenced by n }.

2. Program dependence graph
In the PDG there exist two kinds of dependence:
 One is control dependence, it describes in a program the
conditional statements and circular statements with the
statements embedded in them, their control relationships.
 The other kind is data dependence, it describes in the
assignment statements the left value to the right value
dependence relationship.

3. Program dependence graph
Example for program and its PDG:
void sum{
int i, sum;
sum=0;
i=1;
while(i<11){
sum=sum+i;
i=i+1;
}}

4. Program dependence graph
Result ：
void sum{
int i;
i=1;
while(i<11){
i=i+1;
}}
We just need to left the nodes which
on the left side of assignment
statement contains variable i.

5. • Each PDG has nodes for
– entry point
– procedure parameters and function result
• Each call site has nodes for
– call
– arguments and function result
• Appropriate edges
– entry node to parameters
– call node to arguments
– call node to entry node
– arguments to parameters
How is an SDG Created?

6. SDG for the Sum Program
Enter main
sum = 0 i = 1 while(i < 11) printf(sum) printf(i)
Call add Call add
xin = sum yin = i sum = xout xin = i yin= 1 i = xout
Enter add
x = xin y = yin x = x + y xout = x

7. System dependence graph
 PDG is usually used to describe a single application of
the process, but in the actual software development,
there are few program contains only one single process,
the program is usually composed of multiple processes.
 We need a new structure to reflect multiple processes
program, so SDG could describe it.

8. System dependence graph
 We should not only consider the interdependencies of
statements within process, but also to consider the
invocation of the relationship between process and
process, process parameters between transitive relation,
etc.
 SDG is extended by PDG, it can be expressed as PDG
and a series of process get together as a set.

9. System dependence graph
Through the following steps to construct a system
dependence graph, first of all, on the basis of PDG
increased some new nodes:
(1) For each of the called process set an Entry node
(2) For each argument set an Actual - in node finally set an
Actual - out node together, their relationship with the call
statement is control dependence.
(3) For each parameter set a Formal - in node, if the
parameter value is changed in the procedure call, then
again for this row and add a Formal - out node.

10. The dependence relationship
between new nodes and original
nodes
Called
statement
node
Actual-in
node
Actual-out
node
Process
Entry
node
Formal-out
node
Process Entry
node
Call
relationship
N/A N/A N/A N/A
Actual-in node Control
dependenc
e
N/A N/A N/A N/A
Actual-out node Control
dependenc
e
Summary
relationship
Summary
relationship
N/A
Formal-in node N/A Parameter-
in(data
dependenc
Parameter-
in(data
dependenc
Control
dependenc
e
Parameter-
in(data
dependence)

11. System dependence graph
Example:

13. System dependence graph
Result:

14. END