1. S : S1 B {S.even = B.even}
     | B   {S.even = B.even}
   B : 0  {B.even = true}
     | 1  {B.even = false}


   // A binary number is divisible by 3 if the diff of the odd-bits sum
   // and even-bits sum is divisible by 3.
   S : E  {S.d3 = E.d3}
     | O  {S.d3 = O.d3}
   E : E Pair  {E.diff = Pair.diff + E1.diff; E.d3 = E.diff % 3}
      | Pair {E.d3 = Pair.diff % 3}
   Pair : B1 B2 {Pair.diff = B1.bit - B2.bit}
   O : E B {O.diff = E.diff - B.bit; O.d3 = O.diff %3}
      | B {O.d3 = !B.bit}
   B : 0  {B.bit = 0}
     | 1  {B.bit = 1}

2. 
receive n (val)
L0:
t1 = n % 3
t2 = t1 == 0;
if (t2) goto L1
t3 = t1 == 1;
if (t3) goto L2
goto L3;
L1: 
t4 = a[i];
t5 = j + 1;
j = t5;
t6 = n + 1;
t4[t5] = t6;
n = t6;

goto L3:
L2:
t7 = a[i]
n = n + 1;
t7[j] = n;
i = i + 1;
goto L3:

L3: tx = n < 100
if (tx) goto L0;
return n;

2 (Bonus)
receive q; // q is an array
int x[2];
x[0] = 5;
t1 = x[1];
q[0] = t1

3. 
Note: 1. else attaches to nearest if
      2. in the for loop the increment happens as the last instruction in the loop-body.
      3. goto takes a single argument.

4. a) we have the extend the liveness info to each of the instructions.
   b) we have to carefully compute the BB "def" and "use", by doing a liveness analysis for the basic block first. For instance:
	b = a;
  	x = b
    In this example, b and x are "def" in the BB, and 'a' is "used" in the BB. But not b.