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.
+
+