00:01
We are asked to construct a deterministic finite state automaton that recognizes the set of all bit strings that begin and end with 1 -1.
00:14
So this is going to be a set of all strings, s, which is 1 -1, 0, 1 -1, star, and 1 -1.
00:33
Now, let s -0 be a start state.
00:43
Now, we have the empty string is not in the set s, so it follows that s0 is not a final state.
01:01
Let's consider several other states.
01:04
So we have the state s1 represents that the first digit is a 1.
01:34
State s2 represents that the second bit is a 1, and at the last 2 bits are 1 -1 as well.
01:54
So this is actually instead of just saying the second bit is one, we'll say the first two bits are one and the last two bits are 1 -1.
02:26
So we have that this is going to be a final state.
02:36
S3 represents that the first digit is 0, where the first two digits are 0 .1, first bit 0, first 2 bits 0.
02:57
This is not going to be a final state.
03:02
S4 represents that the last two digits are 0.
03:19
In case the first two bits are 1.
03:24
And s5 represents the last two bits are 01...