Program%20Slicing:%20Theory%20and%20Practice

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Program SlicingTheory and Practice

• Tibor Gyimóthy
• Department of Software Engineering
• University of Szeged

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Co-authors

• Árpád Beszédes
• David Binkley(USA)
• Bogdan Korel(USA)
• János Csirik
• Sebastian Danacic(UK)
• Csaba Faragó
• István Forgács
• Peter Fritzson(S)
• Tamás Gergely
• Tamás Horváth
• Mark Harman(UK)

• Judit Jász
• Mariam Kamkar(S)
• Ákos Kiss
• Gyula Kovács
• Ferenc Magyar
• Jan Maluszynski(S)
• Jukka Paakki(FI)
• Nahid Shahmehri(S)
• Zsolt Szabó
• Attila Szegedi
• Gyöngyi Szilágyi

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Motivation

• Primary initial goal of slicing was to assist
  with debugging.
• Programmers naturally form program
  slices,mentally, when they debug and understand
  programs.
• A program slice consists of the parts of a
  program that potentially affect the values
  computed at some point of interest (slicing
  criteria).

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Example
1. x1 2. i0 3. while (ilt2) 4. i 5.
if (ilt2) 6. x2 else 7. x3 8.
zx
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Example

• Slicing criterion (8,z)
• Which statements have a direct or inderect effect
  on variable z.
• Backward slice consists of all statements that
  the computation at the slicing criteria may
  depend on.
• Forward slice includes all statements depending
  on the slicing criterion.
• Static slice all possible executions of the
  program are taken into account.
• Dynamic slice is constructed with respect to only
  one execution of the program (iteration number is
  taken into account).
• Dynamic slicing criteria (x,i,V,k).
• Example (_,8,z,2)

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Slicing methods

• Weisers original approach iteration of dataflow
  equations (executable slices)
• The most popular approaches are based on
  dependency graphs (non-executable slices)
• Slicing is a simple graph reachability problem

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Program Dependence Graph
1. x1 2. i0 3. while (ilt2) 4. i 5.
if (ilt2) 6. x2 else 7. x3 8.
zx
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Interprocedural Slicing (Calling context problem)
Proc A Proc B Proc C(x,y)

Call C(a,b) Call C(d,e) yx

end end end

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Interprocedural Slicing (Calling context problem)
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Interprocedural Slicing (Calling context problem)

• Summary edges represent the transitive
  dependences due to procedure calls.
• Slices are computed by doing a two phase
  traversing on the System Dependence Graph.
• The main problem is the effective computation of
  the summary edges.
• Forgács I, Gyimóthy T An Efficient
  Interprocedural Slicing Method for Large
  Programs, Proceedings of SEKE'97, the 9th
  International Conference on Software Engineering
  Knowledge Engineering, 1997, Madrid, Spain,
  pp2287

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Slicing approaches for programming languages

• Logic programs
• Gyimóthy, T., Paakki, J. Static Slicing
  of Logic Programs, Proceedings of AADEBUG'95, 2nd
  International Workshop on Automated and
  Algorithmic Debugging, St. Malo, France, 22-24
  May 1995, IRISA/INSA, (Ed. Ducassé, M.), pp.
  85-105
• Gy. Szilágyi, J. Maluszynski and T.
  Gyimóthy. Static and Dynamic Slicing of
  Constraint Logic Programs. Journal Of Automated
  Software Engineering, 9 (1), 2002, pp. 41-65.
• Binary programs
• Á. Kiss, J. Jász and T. Gyimóthy. Using
  Dynamic Information in the Interprocedural Static
  Slicing of Binary Executables. Software Quality
  Journal, 13 (3), September 2005, pp. 227-245,
  Springer Science Business Media, 2005.
• Java programs
• Kovács Gy, Magyar F, Gyimóthy T Static
  Slicing of JAVA Programs, Proceedings of
  SPLST'97, Fifth Symposium on Programming
  Languages and Software Tools, Jyväskylä, 7-9 June
  1997, Finland, pp. 116-128

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Difficult slicing problems

• Slicing arrays
• Precise slice requires distinquishing the
  elements of arrays (dependence analysis).
• Slicing pointers
• Two or more variables refer to the same memory
  location (aliasing problem).

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Dynamic Slicing

• Only one execution is taken into account.
• KorelLaski proposed a data-flow approach to
  compute dynamic slices.(executable slices)
• AgrawalHorgan developed an approach for using
  dependence graphs to compute non-executable
  slices.(size problem)

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Dynamic Dependence Graph
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Dynamic slicing

• Forward global computation of dynamic slices
• Gyimóthy T, Beszédes Á, Forgács I An
  Efficient Relevant Slicing Method for Debugging.
  In Proceedings of the Joint 7th European Software
  Engineering Conference and 7th ACM SIGSOFT
  International Symposium on the Foundations of
  Software Engineering (ESEC/FSE'99),
• Beszédes Á, Gergely T, Szabó ZsM, Csirik J,
  and Gyimóthy T Dynamic Slicing Method for
  Maintenance of Large C Programs, In Proceedings
  of the 5th European Conference on Software
  Maintenance and Reengineering (CSMR 2001), (Eds
  Sousa P, Ebert J), IEEE Computer Society, 2001,
  pp 105-113, Lisbon, Portugal, March 14-16, 2001.
  Certified as the best paper of the conference. 

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Relevant slicing

• 1. x1
• 2. i0
• 3. if igt0 then
• 4. x2
• 5. zx
• Gyimóthy T, Beszédes Á, Forgács I An Efficient
  Relevant Slicing Method for Debugging. In
  Proceedings of the Joint 7th European Software
  Engineering Conference and 7th ACM SIGSOFT
  International Symposium on the Foundations of
  Software Engineering (ESEC/FSE'99)

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Union slices

• Union slice is the union of dynamic slices for a
  set of test cases.
• Á. Beszédes, Cs. Faragó, Zs. M. Szabó, J. Csirik
  and T. Gyimóthy. Union Slices for Program
  Maintenance. Proceedings of the International
  Conference on Software Maintenance (ICSM 2002),
  Montréal, Canada, October 3-6, 2002, IEEE
  Computer Society, 2002, pp. 12-21

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Union slices
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Applications

• Debugging
• Regression testing
• Software maintenance
• Architecture reconstruction
• Identify reusable functions
• Reverse engineering
• Slice metrics
• Program comprehension

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Theory of program slicing

• David Binkley, Sebastian Danicic, Tibor Gyimóthy,
  Mark Harman, Ákos Kiss, and Bogdan Korel. A
  Formalisation of the Relationship between Forms
  of Program Slicing. Science of Computer
  Programming, 2006. Accepted for publication.
• David Binkley, Sebastian Danicic, Tibor Gyimóthy,
  Mark Harman, Ákos Kiss, and Bogdan Korel.
  Theoretical Foundations of Dynamic Program
  Slicing. Theoretical Computer Science, 2006.
  Accepted for publication.
• Dave Binkley, Sebastian Danicic, Tibor Gyimóthy,
  Mark Harman, Ákos Kiss, and Bogdan Korel. Minimal
  Slicing and the Relationships between Forms of
  Slicing. In Proceedings of the 5th IEEE
  International Workshop on Source Code Analysis
  and Manipulation (SCAM 2005), pages 45-54,
  September 30 - October 1, 2005. Best paper award.
• Dave Binkley, Sebastian Danicic, Tibor Gyimóthy,
  Mark Harman, Ákos Kiss, and Lahcen Ouarbya.
  Formalizing Executable Dynamic and Forward
  Slicing. In Proceedings of the 4th IEEE
  International Workshop on Source Code Analysis
  and Manipulation (SCAM 2004), pages 43-52,
  September 15-16, 2004.IEEE Computer Society, 2004.

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Background

• Informally
• A static slice preserves a projection of the
  semantics of the original program for all
  possible inputs.
• A dynamic slice preserves the effect of the
  program for a fixed input.
• Thus, a static slice is expected to be a valid
  (even if an overly large) dynamic slice.

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Counter Example

• 1 x 1
• 2 x 2
• 3 if (xgt1)
• 4 y 1
• 5 else
• 6 y 1
• 7 z y
• Original program

• 1 x 1
• 3 if (xgt1)
• 4 y 1
• 5 else
• 6 y 1
• 7 z y
• A static slice w.r.t. (y,7)

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Counter Example

• 1 x 1
• 2 x 2
• 3 if (xgt1)
• 4 y 1
• 5 else
• 6 y 1
• 7 z y
• The original program

• 1 x 1
• 3 if (xgt1)
• 4 y 1
• 5 else
• 6 y 1
• 7 z y
• A static slice w.r.t. (y,7)

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Explanation

• The reason is in the details of the definitions.
• Static slicing, as defined by Weiser, does not
  care about the path of execution.
• Dynamic slicing of Korel Laski requires the
  path to be same in the original program and in
  the slice.

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Motivation

• So, our common knowledge does not fit to the
  original definitions.
• We have to find out why?
• Thus, we provide a formal theory, which helps us
  to answer this question, i.e., which helps us to
  compare existing slicing techniques.

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The Program Projection Theory

• Syntactic ordering ()
• A partial order on programs.
• Describes a property slicing minimizes on.
• Semantic equivalence ()
• An equivalence relation on programs.
• Describes a property slicing keeps invariant.
• Projection ((,)) describes slicing.

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Syntactic Orderings

• Traditional sytanctic ordering () a program q
  is smaller than p if it can be obtained by
  deleting statements from p.
• Other orderings are possible, e.g., amorphous
  slicing uses an ordering based only on the number
  of statements.

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Semantic Equivalences

• Can be defined by parameterizing a unified
  equivalence relation, U(S,V,P,X), which compares
  projections of state trajectories.
• S the set of initial states for which the
  trajectories have to be equal.
• V the set of variables of interest.
• P the set points of interest in the trajectory
  (line number and occurance of statement of
  interest).
• X a function on a pair of programs, determining
  which statements shall be kept in the trajectory
  (this captures the trajectory requirement of KL).

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Instantiations of the Framework

• Parameterizations of a unified equivalence
  relation.
• S(V,n) U(S,V,n?N,e)
• DKLi(s,V,n(k)) U(s,V,n(k),?)

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Example
1 x 1 2 x 2 3 if (xgt1) 4 y 1 5 else 6 y 1 7 z y Program p 1 x 1 3 if (xgt1) 4 y 1 5 else 6 y 1 7 z y Program q

• Tp(1,)(2,x1)(3,x2)(4,x2)(7,x2,y1)
• Tq(1,)(3,x1)(6,x1)(7,x1,y1)

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Example
1 x 1 2 x 2 3 if (xgt1) 4 y 1 5 else 6 y 1 7 z y Program p 1 x 1 3 if (xgt1) 4 y 1 5 else 6 y 1 7 z y Program q

• ?S(Tp)(7,y1)
• ?S(Tq)(7,y1)

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Example
1 x 1 2 x 2 3 if (xgt1) 4 y 1 5 else 6 y 1 7 z y Program p 1 x 1 3 if (xgt1) 4 y 1 5 else 6 y 1 7 z y Program q

• ?D(Tp)(1,_)(3,_)(4,_)(7,y1)
• ?D(Tq)(1,_)(3,_)(6,_)(7,y1)

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Comparison

• Once the formal descriptions of slicing
  techniques is available, they can be compared.
• Subsumes relation A-slicing subsumes B-slicing
  iff all B-slices are valid A-slices as well.

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Subsumes Relation
dynamic slicing as defined by Korel and Laski
traditional static slicing
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Minimal Slices

• We moved on to investigate another relation
  between slicing techniques which have smaller
  minimal slices than the others.
• Slice minimality is defined in terms of the
  syntactic ordering.
• Ranking slicing techniques A-slicing is of lower
  (or equal) rank than B-slicing iff for all
  minimal B-slices there exists a smaller minimal
  (or equal) A-slice.

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Rank Relation
traditional static slicing
dynamic slicing as defined by Korel and Laski
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Example
1 x 1 2 x 2 3 if (xgt1) 4 y 1 5 else 6 y 1 7 z y The original program 4 y 1 7 z y A minimal static slice The minimal KL-dynamic slice 6 y 1 7 z y Another minimal static slice

• There is no minimal KL-dynamic slice, which is
  smaller than or equal to the second minimal
  static slice.

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Relations
Rank relation
Subsumes relation

• We found (and proved) that rank is the dual
  concept of subsumes relationship.
• If a slicing subsumes another one then it is of
  lower rank.

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Summary of Results

• Static slicing and KL-dynamic slicing are
  incomparable in the subsumes relation (A static
  slice is not always a valid dynamic slice)
• Subsumes and rank are dual concepts
• Static slicing and KL-dynamic slicing are
  incomparable in the rank relation (It is not
  always possible to find a minimal KL-dynamic
  slice, which is smaller than, or equal to, a
  minimal static slice)

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Current Challenges

• There is no established common notation.
• How to deal with non-terminating programs?
  (Transfinite trajectories? Other solutions?)
• Which other slicing techniques can be formalized
  with this framework?
• What operations can we perform on sets of slices
  and what are their result?
• How do these results apply to schemas?