Consider the following C program:

#include < stdio.h >
  int counter = 0;
  int calc (int a, int b) {
  int c;
  counter++;
  if (b==3) return (a*a*a);
  else {
    c = calc(a, b/3);
    return (c*c*c);
 }
}
int main (){
  calc(4, 81);
  printf ("%d", counter);
}

The output of this program is _____.

Consider the following C code. Assume that unsigned long int type length is 64 bits.

unsigned long int fun(unsigned long int n){
     unsigned long int i, j = 0, sum = 0;
     for (i = n; i > 1; i = i/2) j++;
     for ( ; j > 1; j = j/2) sum++;
     return(sum);
}

The value returned when we call fun with the input $${2^{40}}$$ is

The set of all recursively enumerable languages is

Let $$N$$ be an $$NFA$$ with $$n$$ states. Let $$k$$ be the number of states of a minimal $$DFA$$ which is equivalent to $$N.$$ Which one of the following is necessarily true?