1. Survey of program slicing techniques
Presenter’s Name: Keyur Malaviya

2. Purpose of this paper
It’s a survey that presents an overview of program slicing
Various general approaches used to compute slices
Specific techniques used to address procedures, unstructured control flow, composite data types and pointers, and concurrency.
Static and dynamic slicing methods for each of these features
Comparison and classification in terms of their accuracy and efficiency

3. Topics Covered Definitions Static slicing vs Dynamic slicing
Basic slicing algorithm for single procedure and multiprocedure
Weiser Algorithm
Hausler
Bergeretti and Carr´e
Horwitz, Reps, and Binkley Algo
Applications

4. Definitions (Basics) Slicing? Slicing Criteria?
Static and Dynamic slicing?
Program slicing?
Program dependence graph (PDG) or
Control flow graph (CFG) or
System dependency grapy (SDG)
(1) read(n);
(2) i := 1;
(3) sum := 0;
(4) product := 1;
(5) while i <= n do
begin
(6) sum := sum + i;
(7) product := product * i;
(8) i := i + 1
end;
(9) write(sum);
(10) write(product)

5. Definitions (CFG \ PDG)
PDG: Directed graph; Vertices = statements and control predicates
Edges = data and control dependences
CFG

6. Definitions
Program slice: consists of the parts of a program that affect the values computed at some point of interest.
Slicing criterion: is this point of interest specified by a pair (program point, set of variables)
Original concept by Weiser: Its a mental abstractions that people make when they are debugging a program
Static slicing: Computed without making assumptions regarding a program’s input
Dynamic slicing: Relies on some specific test case

7. Definitions (criteria and slicing )
Slice of this program w.r.t criterion (10, product)
(1) read(n);
(2) i := 1;
(3) sum := 0;
(4) product := 1;
(5) while i <= n do
begin
(6) sum := sum + i;
(7) product := product * i;
(8) i := i + 1
end;
(9) write(sum);
(10) write(product)
(1) read(n);
(2) i := 1;
(3) sum := 0;
(4) product := 1;
(5) while i <= n do
begin
(6) sum := sum + i;
(7) product := product * i;
(8) i := i + 1
end;
(9) write(sum);
(10) write(product)
(1) read(n);
(2) i := 1;
(3)
(4) product := 1;
(5) while i <= n do
begin
(6)
(7) product := product * i;
(8) i := i + 1
end;
(9)
(10) write(product)
Single-procedure programs (PDG); Shading in the PDG shown before  vertices in the slice w.r.t. write(product)

8. Static slicing vs Dynamic slicing
Dynamic Slicing: First introduced by Korel and Laski
Non-interactive variation of Balzer’s flowback analysis
Only the dependences that occur in a specific execution of the program are taken into account
Dynamic slicing criterion is a triple (input, occurrence of a statement, variable) – it specifies the input, and distinguishes between different occurrences of a statement in the execution history
Dynamic slicing assumes fixed input for a program
Static slicing does not make assumptions regarding the input.
Flowback analysis: Interactively traverse a graph (data and
control dependences between statements in the program); For
e.g.: S(V) depends on T(V), S and T are statements; T  S is
in CFG, then trace back from vertex for S to vertex for T

9. Static slicing vs Dynamic slicing criterion SS: (8, x) and DS: (n=2, 81, x)
Example program:
Static slice w.r.t. criterion (8, x)
Dynamic slice w.r.t. criterion (n=2, 81, x)
read(n);
i := 1;
while (i <= n) do
begin
if (i mod 2 = 0) then
x := 17
else
x := 18;
i := i + 1
end;
write(x) 1 2 3 4 5 6 7 8
read(n);
i := 1;
while (i <= n) do
begin
if (i mod 2 = 0) then
x := 17
else
x := 18;
i := i + 1
end;
write(x)
read(n);
i := 1;
while (i <= n) do
begin
if (i mod 2 = 0) then
x := 17
else ;
i := i + 1
end;
write(x)

10. Slicing Algorithm Approaches
Achieved through one of three algorithmic approaches:
1) data-flow equations
2) system dependency graph
3) parallel algorithm
All based on control and data dependencies and defined in terms of a graph representation of a program (as seen before)

11. Approaches:
Weiser’s approach: compute slices from consecutive sets of transitively relevant statements ( data flow and control flow dependences )
Ottenstein approach: in terms of a reachability problem in a PDG.
Slicing criterion  A vertex in the PDG;
A Slice corresponds to all PDG vertices from which the vertex under consideration can be reached
Other approaches: Based on modified and extended versions of PDGs
Statements and control predicates are gathered by
way of a backward traversal of the program’s
control flow graph (CFG) or PDG, starting at the
slicing criterion

12. Weiser Algorithm (single procedure)
Two levels of iteration:
1. Transitive data dependences in the presence of loops in the program
2. Control dependences, initiating the inclusion of control predicates for which each, step 1 is repeated to include the statements it is dependent upon
Determine directly relevant variables and then indirectly relevant variables; From these compute the sets of relevant statements

13. Parameters and equations
Defined and Referenced Variables
DEF(i) and REF(i)
Say at node ‘i’ consider a statement
a = b + c
Then DEF(i) = {a} and REF(i) = {b, c}
Directly Relevant Variable
: set of directly relevant variables,
where slice criterion = (V, n)
Set DRV (i)  Set DRV (all nodes j) that have a direct edge to i,

14. Parameters and equations
Directly Relevant Statements
: set of all nodes i that define a variable v that is relevant at the successor node of I
Indirectly Relevant Variables
referenced variables in control predicate are indirectly relevant when at least one of the statements in its body is relevant, denoted:
b is known as a range of influence INFL (b),

15. Example program

16. Applying the Weiser algo
Slicing criterion (10, product) & our example program
NODE
DEF 1
{n} 2
{i} 3
{sum} 4
{product} 5 6 7 8 9 10
REF
{i, n}
{sum, i}
{product, i}
{i}
{sum}
{product}
INFL
{6, 7, 8} R0
{product}

17. Applying the Weiser algo
Slicing criterion (10, product) & our example program
NODE
DEF 1
{n} 2
{i} 3
{sum} 4
{product} 5 6 7 8 9 10
REF
{i, n}
{sum, i}
{product, i}
{i}
{sum}
{product} R0
{product}
{product}
{product}

18. Applying the Weiser algo
Slicing criterion (10, product) & our example program
NODE
DEF 1
{n} 2
{i} 3
{sum} 4
{product} 5 6 7 8 9 10
REF
{i, n}
{sum, i}
{product, i}
{i}
{sum}
{product} R0
{product, i}
{product}
{product}
{product}

19. Applying the Weiser algo
Slicing criterion (5, {i, n}) & repeat the same procedure
Slicing criterion (10, product) & our example program
NODE
DEF 1
{n} 2
{i} 3
{sum} 4
{product} 5 6 7 8 9 10
REF
{i, n}
{sum, i}
{product, i}
{i}
{sum}
{product} R0
{i}
{product, i}
{product}
{n}
{i, n}
{i, n}
{product, i, n}
{product, i, n}
{product, i, n}
{product, i, n}
{product}
{product}

20. Applying the Weiser algo
Slicing criterion (10, product) & our example program
NODE
DEF 1
{n} 2
{i} 3
{sum} 4
{product} 5 6 7 8 9 10
REF
{i, n}
{sum, i}
{product, i}
{i}
{sum}
{product}
INFL
{6, 7, 8} R0
{i}
{product, i}
{product} R1
{n}
{i, n}
{product, i, n}
{product} ? ? ?

21. Equations for related statements:

22. Hausler (functional style)
For each type of statement, have a function
and
& express how a statement transforms the set of relevant variables & relevant statements reply.
Functions for a while statement are obtained by transforming it into an infinite sequence of if statements

23. Information-flow relations (Bergeretti and Carr´e)
Statement S:
variable v and
an expression e
( e can be control predicate or right-hand side of assignment)
We define relations:
They possess following properties:
 iff the value of v on entry to S potentially
affects the value computed for e
 iff the value computed for e potentially
affects the value of v on exit from S,
 iff the value of v on entry to S may affect
the value of v on exit from S.

24. Information-flow relations (Bergeretti and Carr´e)
How to get the slice with respect to the final value of v ?
The set of all expressions e for which can be used to construct “partial statements”  replace all statements in S that do not contain expressions in by empty statements.
Relations are computed in a syntax-directed, bottom-up
For S, v := e

25. Information-flow relations (Bergeretti and Carr´e)
Set of expressions that potentially affect the value of product at the end of the program are {1, 2, 4, 5, 7, 8}
Partial statement is obtained
by omitting all statements from the program that do not contain expressions in this set, i.e., both assignments to sum and both write statements
The slice is same as Weiser’s algorithm

26. Dependence graph based approaches (PDG) and Procedures
PDG variant of Ottenstein shows considerably more detail than that by Horwitz, Reps, and Binkley
Procedures
Call-return structure of interprocedural execution paths
Single pass considers infeasible execution paths – a problem called “calling-context”
Will see two approaches:
Weiser’s approach (CFG)
Horwitz, Reps, and Binkley (SDG)

27. Dependence graph based approaches (PDG) and Procedures
Weiser’s approach for interprocedural static slicing:
Interprocedural summary information is computed, using previously developed techniques
 P, set MOD(P) of variables = modified by P, and set USE(P) of variables = used by P
Intraprocedural slicing algorithm: Treat ‘P()’ as a conditional assignment statement ‘if SomePredicate then MOD(P) := USE(P)’ (external procedures, source-code is unavailable?)

28. Weiser’s approach (i) procedures Q called by P:
Actual inter-procedural slicing algo that generates new slicing criteria iteratively w.r.t slices computed in step (2):
(i) procedures Q called by P:
(i) procedures Q called by P
(i) procedures Q called by P: consist of all pairs
(ii) procedures R that call P
(ii) procedures R that call P: consist of all pairs
(ii) procedures R that call P:

29. Weiser’s Algo To formalize the generation of new criteria:
UP(S) : Map (a set S of slicing criteria in a P) to
(a set of criteria in procedures that call P)
DOWN(S): Map (a set S of slicing criteria in a P) to
(a set of criteria in procedures called by P)
Set of all criteria: transitive and reflexive closure of the UP and DOWN relations (UP U DOWN)*
UP and DOWN sets: Requires sets of relevant variables to be known at all call sites  computation of these sets is done by slicing these procedures
When iteration stops?
When no new criteria are generated

30. Main issue: procedure P(y1, y2, … , yn); program Main; begin …
write(y1);
write(y2); …
(M) write(yn)
end
program Main; …
while ( ) do
P(x1, x2, , xn);
z := x1;
x1 := x2;
x2 := x3;
xn1 := xn
end;
(L) write(z)
end
Procedure P is sliced ‘n’ times by Weiser’s algorithm for criterion (L, {z}).

31. Weiser’s Algo Lprogram point at S = write(z)
M  program point at last statement in P
Slice w.r.t. criterion (L, { z })?
‘n’ iterations of the body of the while loop
During the ith iteration, variables x1, …, xi will be relevant at call site
DOWN(Main): criterion (M, { y1, …, yi }) gets included
Issue is: ???
Procedure P will be sliced n times

32. What was the problem?
Weiser’s algorithm does not take into account which output parameters are dependent on which input parameters is a source of imprecision
Lets see another examples that shows this problem:

33. What was the problem? a := 17; program Example; begin (1) a := 17;
(3) P(a, b, c, d);
(4) write(d)
end
procedure P(v, w, x, y);
(5) x := v;
(6) y := w
program Example;
begin ;
b := 18;
P(a, b, c, d);
write(d)
end
procedure P(v, w, x, y);
y := w
program Example;
begin
a := 17;
a := 17;
b := 18;
P(a, b, c, d);
end
procedure P(v, w, x, y); ;
y := w
end
Actual Slice
Slice with Weiser’s algo

34. Horwitz, Reps, and Binkley Algo
Computes precise inter-procedural static slices:
1. SDG, a graph representation for multi-procedure programs
2. Computation of inter-procedural summary information
precise dependence relations between i/p & o/t parameters
explicitly present in SDG as summary edges
3. Two-pass algorithm for extracting interprocedural slices from an SDG

35. Multi-procedure program

36. Horwitz, Reps, and Binkley Algo 1) Structure of SDG
SDG = PDG for main program, & a procedure dependence graph for each procedure
SDG <> PDG (Vertices and edges are different)
For each call statement, there is a call-site vertex in the SDG as well as actual-in and actual-out vertices

37. 1) Structure of SDG interprocedural dependence edges:
Each procedure dependence graph has an entry vertex, and formal-in and formal-out vertices
interprocedural dependence edges:
(i) control dependence edge (call-site vertex & entry vertex) (ii) parameter-in edge between corresponding actual-in and formal-in vertices,
(iii) a parameter out edge between corresponding formal-out and actual-out vertices, and (iv) summary edges that represent transitive interprocedural data dependences

38. 1) Structure of SDG

39. Horwitz, Reps, and Binkley Algo 2) and 3)
Second part:
Models the calling relationships between the procedures (as in a call graph)
Compute subordinate characteristic graph
For each procedure in the program, this graph contains edges that correspond to precise transitive flow dependences between its input and output parameters.
Third part:
summary edges of an SDG serve to circumvent the calling context problem
First phase: all vertices from which ‘s’ can be reached without descending into procedure calls (slicing starts at vertex s)
Second phase: remaining vertices in the slice by descending into all previously side-stepped calls

40. COMPLETE SDG
NEXT: Complete SDG for the example program shown above

42. SDG style interpretation
Thin solid arrows  represent flow dependences,
Thick solid arrows  correspond to control dependences,
Thin dashed arrows  Used for call, parameter-in, and parameter-out dependences,
Thick dashed arrows  Transitive inter-procedural flow dependences.
Shaded vertices Vertices in the slice w.r.t. statement write(product)
Light shading  Vertices identified in the first phase
Dark shading  Vertices identified in the second phase

43. The slice with criteria (10, product)
program Example;
begin
(1) read(n);
(2) i := 1;
(3) sum := 0;
(4) product := 1;
(5) while i <= n do
(6) Add(sum, i);
(7) Multiply(product, i);
(8) Add(i, 1)
end;
(9) write(sum);
(10) write(product)
end
procedure Add(a; b);
begin
11) a := a + b
End
procedure Multiply(c; d);
12) j := 1;
13) k := 0;
14) while j <= d do
15) Add(k, c);
16) Add(j, 1);
end;
17) c := k
end

44. Application of slicing
Debugging and program analysis
Program differencing and program integration
analyzing an old and a new version of a program
partitioning the components
compares slices in order to detect equivalent behaviors
Software maintenance
change at some place in a program  behavior of other parts of the program

45. QUESTIONS