**commit** 9c80370585ba560640ed71ac2f628466970f9392
**parent** c6b9e58c6fb7da3d1d0b6cc5f9ac7b4a596db46d
**Author:** Agastya Chandrakant <acagastya@outlook.com>
**Date:** Mon, 16 Apr 2018 20:55:07 +0530
add
**Diffstat:**

1 file changed, 8 insertions(+), 2 deletions(-)

**diff --git a/s4/fafl/report.md b/s4/fafl/report.md**
@@ -30,7 +30,7 @@ function newModulo(u, v) {
```
In the above code, `quo` variable gives the quotient. Noting that repeated subtraction yields remainder, and count of subtraction yields quotient, state transition diagram of a STM with infinite memory (in theory) can be drawn.
-__Refer figure for TM1 which acts as a transducer to find remainder and quotient of two natural numbers__
+__Refer figure 1 for TM1 which acts as a transducer to find remainder and quotient of two natural numbers__
### STM to check if entered natural number is prime or not
@@ -43,8 +43,14 @@ Consider a natural number `num`. If it is a composite number, it has atleast one
### Performance analysis
#### For calculation of remainder and quotient
-#### To find if the number is prime
+#### To find if the number is prime
+For an input `num`, the first step is to make a copy of $\lfloor\dfrac{num}{2}\rfloor$ start reading the tape from the beginning.
+1. For every second `1` encountered, mark it as `D`.
+2. Move right until `B` is found.
+3. Update `B` as `1`.
+4. Move right and add `B` to the array.
+5. Repeat steps 1 - 4 until instruction pointer reaches `0`. The complexity is observed to be $O(n)$.
### Output
#### Result #1
#### Result #2