1. Worst case complexity of Andersen *x = y x abc y def x abc y def Worst case: N 2 per statement, so at least N 3 for the whole program. Andersen is in fact O(N 3 )

2. New idea: one successor per node Make each node have only one successor. This is an invariant that we want to maintain. x a,b,c y d,e,f *x = y x a,b,c y d,e,f

3. x *x = y y More general case for *x = y

4. x *x = y yxyxy More general case for *x = y

5. x x = *y y Handling: x = *y

6. x x = *y yxyxy Handling: x = *y

7. x x = y y x = &y xy Handling: x = y (what about y = x?) Handling: x = &y

8. x x = y yxyxy x = &y xyx y,… xy Handling: x = y (what about y = x?) Handling: x = &y get the same for y = x

9. Our favorite example, once more! S1: l := new Cons p := l S2: t := new Cons *p := t p := t 1 2 3 4 5

10. Our favorite example, once more! S1: l := new Cons p := l S2: t := new Cons *p := t p := t l S1 t S2 p l S1 l p l t S2 p l S1,S2 tp 1 2 3 4 5 12 3 l S1 t S2 p 4 5

11. Flow insensitive loss of precision S1: l := new Cons p := l S2: t := new Cons *p := t p := t l t S1 p S2 l t S1 p S2 l t S1 p S2 l t S1 p S2 Flow-sensitive Subset-based Flow-insensitive Subset-based l t S1 p S2 l S1,S2 tp Flow-insensitive Unification- based

12. bar() { i := &a; j := &b; foo(&i); foo(&j); // i pnts to what? *i :=...; } void foo(int* p) { printf(“%d”,*p); } 1 2 3 4 Another example

13. bar() { i := &a; j := &b; foo(&i); foo(&j); // i pnts to what? *i :=...; } void foo(int* p) { printf(“%d”,*p); } i a j b p i a i a j b i a j b p i,j a,b p 1 2 3 4 12 Another example 4 3