complement in 11.13

notes/8.md

@@ -64,4 +64,36 @@ Analysis of Reaching Definition
 
 Effect of an Instruction
 
-`IN[b]` and `OUT[b]`
+`IN[b]` and `OUT[b]`
+
+Meet Operator 
+
+`IN[b] = union(OUT[p1]...OUT[pn])`
+
+```c
+// init
+OUT[entry] = {}
+
+
+
+```
+
+## Liveness Analysis
+
+Liveness is the concept the variable is used in the future. It helps **eliminating dead code**.
+
+Transfer function
+
+* `USE[b]` set of variables used in `b`
+* `DEF[b]` set of variables defined in `b`
+
+so transfer function `f_b` for a basic block b:
+```IN[b] = USE[b] + (OUT[b] - DEF[b])```
+
+for reaching defintion
+
+```OUT[b] = union(INs)```
+
+For supporting cyclic graphs, repeated computation is needed.
+
+

notes/9.md

@@ -0,0 +1,28 @@
+# Control Flow Analysis
+
+Dominator
+
+for a given CFG **a node `x` dominates a node `y`** if every path from the Entry block to `y` contains `x`.
+
+* Each BB dominates itself
+* If `x dom y` and `y dom z` then `x dom z`
+* If `x dom z` and `y dom z` then either `x dom y` or `y dom x`
+
+Dominator Tree
+* initial node is a root
+* `x dom y` means that "`y` is a child of `x`"
+
+
+Natural Loops
+
+How to Find Natural Loop?: Introduction Backedge
+
+Important concepts in a loop
+* Header and Loop BB
+* Back Edges
+* Exit Edges
+* Preheader (Preloop)
+
+Loop-Invariant Computation
+
+