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Slicing Unconditional Jumps with Unnecessary Control Dependencies Carlos Galindo Sergio P erez Josep Silva VRAIN Universitat Polit` ecnica de Val` encia, Spain 30th International Symposium on Logic-Based Program Synthesis and

  1. Slicing Unconditional Jumps with Unnecessary Control Dependencies Carlos Galindo Sergio P´ erez Josep Silva VRAIN Universitat Polit` ecnica de Val` encia, Spain 30th International Symposium on Logic-Based Program Synthesis and Transformation September 9th, 2020 C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 1 / 14

  2. Program slicing Program slicing A software analysis technique to extract the statements of a program that affect a given slicing criterion . 1 void main(int n) { 1 void main(int n) { int sum = 0; int sum = 0; 2 2 int prod = 0; int prod = 0; 3 3 int i = 0; int i = 0; 4 4 while (i < 10) { while (i < 10) { 5 5 sum += 1; sum += 1; 6 6 prod += n; prod += n; 7 7 i++; i++; 8 8 } } 9 9 log(sum); log(sum ); 10 10 log(prod ); log(prod ); 11 11 12 } 12 } C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 2 / 14

  3. Program slicing Program slicing A software analysis technique to extract the statements of a program that affect a given slicing criterion . 1 void main(int n) { 1 void main(int n) { int sum = 0; int sum = 0; 2 2 int prod = 0; int prod = 0; 3 3 int i = 0; int i = 0; 4 4 while (i < 10) { while (i < 10) { 5 5 sum += 1; sum += 1; 6 6 prod += n; prod += n; 7 7 i++; i++; 8 8 } } 9 9 log(sum); log(sum ); 10 10 log(prod ); log(prod ); 11 11 12 } 12 } C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 2 / 14

  4. Program slicing Program slicing A software analysis technique to extract the statements of a program that affect a given slicing criterion . 1 void main(int n) { 1 void main(int n) { int sum = 0; int sum = 0; 2 2 int prod = 0; int prod = 0; 3 3 int i = 0; int i = 0; 4 4 while (i < 10) { while (i < 10) { 5 5 sum += 1; sum += 1; 6 6 prod += n; prod += n; 7 7 i++; i++; 8 8 } } 9 9 log(sum); log(sum ); 10 10 log(prod ); log(prod ); 11 11 12 } 12 } C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 2 / 14

  5. Program slicing Example 1 public void f() { 1 public void f() { 1 public void f() { while (X) { while (X) { while (X) { 2 2 2 if (Y) { if (Y) { if (Y) { 3 3 3 if (Z) { if (Z) { if (Z) { 4 4 4 A; A; A; 5 5 5 break; break; break; 6 6 6 } } } 7 7 7 B; B; B; 8 8 8 break; break; break; 9 9 9 } } } 10 10 10 C; C; C; 11 11 11 } } } 12 12 12 D; D; D; 13 13 13 14 } 14 } 14 } (a) Original program (b) SDG slice (c) Minimal slice C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 3 / 14

  6. Program slicing Example 1 public void f() { 1 public void f() { 1 public void f() { while (X) { while (X) { while (X) { 2 2 2 if (Y) { if (Y) { if (Y) { 3 3 3 if (Z) { if (Z) { if (Z) { 4 4 4 A; A; A; 5 5 5 break; break; break; 6 6 6 } } } 7 7 7 B; B; B; 8 8 8 break; break; break; 9 9 9 } } } 10 10 10 C; C; C; 11 11 11 } } } 12 12 12 D; D; D; 13 13 13 14 } 14 } 14 } (a) Original program (b) SDG slice (c) Minimal slice C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 3 / 14

  7. Program slicing Example 1 public void f() { 1 public void f() { 1 public void f() { while (X) { while (X) { while (X) { 2 2 2 if (Y) { if (Y) { if (Y) { 3 3 3 if (Z) { if (Z) { if (Z) { 4 4 4 A; A; A; 5 5 5 break; break; break; 6 6 6 } } } 7 7 7 B; B; B; 8 8 8 break; break; break; 9 9 9 } } } 10 10 10 C; C; C; 11 11 11 } } } 12 12 12 D; D; D; 13 13 13 14 } 14 } 14 } (a) Original program (b) SDG slice (c) Minimal slice C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 3 / 14

  8. Program slicing The System Dependence Graph CDG CFG PDG SDG Slice DDG Figure: Sequence of graphs generated to produce a slice. Enter h() Enter h() 1 void h() { while (x < 10) while (x < 10) { 2 print(x); while (x < 10) 3 x++; 4 x++ print(x) } 5 print(x) x++ Exit h() 6 } PDG CFG Black: CDG, Red: DDG C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 4 / 14

  9. Program slicing The System Dependence Graph CDG CFG PDG SDG Slice DDG Figure: Sequence of graphs generated to produce a slice. Enter h() Enter h() 1 void h() { while (x < 10) while (x < 10) { 2 print(x); while (x < 10) 3 x++; 4 x++ print(x) } 5 print(x) x++ Exit h() 6 } PDG CFG Black: CDG, Red: DDG C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 4 / 14

  10. Program slicing The System Dependence Graph CDG CFG PDG SDG Slice DDG Figure: Sequence of graphs generated to produce a slice. Enter h() Enter h() 1 void h() { while (x < 10) while (x < 10) { 2 print(x); while (x < 10) 3 x++; 4 x++ print(x) } 5 print(x) x++ Exit h() 6 } PDG CFG Black: CDG, Red: DDG C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 4 / 14

  11. Program slicing The System Dependence Graph CDG CFG PDG SDG Slice DDG Figure: Sequence of graphs generated to produce a slice. Enter h() Enter h() 1 void h() { while (x < 10) while (x < 10) { 2 print(x); while (x < 10) 3 x++; 4 x++ print(x) } 5 print(x) x++ Exit h() 6 } PDG CFG Black: CDG, Red: DDG C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 4 / 14

  12. Program slicing Unconditional jumps ( break , return , goto ) in the CFG void main () { 1 x = 0; 2 while (true) { 3 x++; 4 if (x > 10) 5 break; 6 } 7 print(x); 8 } 9 C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 5 / 14

  13. Program slicing Unconditional jumps ( break , return , goto ) in the CFG void main () { 1 Enter main() x = 0; 2 while (true) { 3 x = 0 x++; 4 if (x > 10) 5 while (true) break; 6 break } 7 x++ if (x > 10) print(x) print(x); 8 } 9 Exit main() CFG: Jumps as arcs C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 5 / 14

  14. Program slicing Unconditional jumps ( break , return , goto ) in the CFG void main () { 1 Enter main() Enter main() x = 0; 2 while (true) { 3 x = 0 x++; 4 x = 0 while (true) print(x) if (x > 10) 5 while (true) break; 6 break } x++ if (x > 10) 7 x++ if (x > 10) print(x) print(x); 8 } 9 Exit main() CFG: Jumps as arcs C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 5 / 14

  15. Program slicing Unconditional jumps ( break , return , goto ) in the CFG void main () { 1 Enter main() Enter main() x = 0; 2 while (true) { 3 x = 0 x++; 4 x = 0 while (true) print(x) if (x > 10) 5 while (true) break; 6 break } x++ if (x > 10) 7 x++ if (x > 10) print(x) print(x); 8 } 9 Exit main() CFG: Jumps as arcs C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 5 / 14

  16. Program slicing Unconditional jumps ( break , return , goto ) in the CFG Enter main() void main () { 1 x = 0; 2 x = 0 while (true) { 3 x++; 4 while (true) if (x > 10) 5 break; 6 x++ if (x > 10) break print(x) } 7 print(x); 8 Exit main() } 9 CFG: Jumps as nodes C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 5 / 14

  17. Program slicing Unconditional jumps ( break , return , goto ) in the CFG Enter main() Enter main() void main () { 1 x = 0; 2 x = 0 while (true) { 3 x = 0 while (true) print(x) x++; 4 while (true) if (x > 10) 5 x++ if (x > 10) break; 6 x++ if (x > 10) break print(x) } 7 print(x); 8 break Exit main() } 9 CFG: Jumps as nodes C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 5 / 14

  18. Program slicing Unconditional jumps ( break , return , goto ) in the CFG Enter main() Enter main() void main () { 1 x = 0; 2 x = 0 while (true) { 3 x = 0 while (true) print(x) x++; 4 while (true) if (x > 10) 5 x++ if (x > 10) break; 6 x++ if (x > 10) break print(x) } 7 print(x); 8 break Exit main() } 9 CFG: Jumps as nodes C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 5 / 14

  19. Program slicing Unconditional jumps ( break , return , goto ) in the CFG void main () { Enter main() 1 x = 0; 2 while (true) { x = 0 3 x++; 4 if (x > 10) 5 while (true) break; 6 } 7 x++ if (x > 10) break print(x) print(x); 8 } 9 Exit main() ACFG: Adds non-exec. arcs to create control deps. C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 5 / 14

  20. Program slicing Unconditional jumps ( break , return , goto ) in the CFG Enter main() void main () { Enter main() 1 x = 0 while (true) x = 0; 2 while (true) { 3 x = 0 x++; 4 x++ if (x > 10) if (x > 10) 5 while (true) break; 6 } 7 x++ if (x > 10) break print(x) break print(x); 8 } 9 Exit main() print(x) ACFG: Adds non-exec. arcs to create control deps. C. Galindo et al. (UPV) Slicing Unconditional Jumps LOPSTR 2020 - September 9th 5 / 14

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