00:01
We are given a turing machine and we are asked given initial tapes to determine final tapes when the machine halts.
00:12
Assuming the machine begins in the initial position.
00:18
So we see that this turing machine has the five tumbles s00 s01 r, s01 s01 s10 r, s0b s1 1l, s1 1 .s1.
00:34
1 s10r and s1b s20l.
00:41
In part a, we are given the initial tape, which has initial configuration, s0101.
01:05
Now what this notation means is that tape is going to be blank except for a portion that reads 0101 from left to right.
01:23
The machine is currently in state s0.
01:25
And the tapehead is reading the first zero.
01:33
In other words, the symbol that is the one following the bracketed state.
01:39
And this is the initial configuration.
01:44
Now, we see that in our turing machine we have the transition s0 -0, s -1 -r.
01:59
And this tells us the next configuration be obtained by replacing the the 0 with a 1 by changing to state s1 and by moving to the right so that new configuration is 1, s1, 101.
02:28
Now we also see that the turing machine contains the transition s11, s10r, and so the next configuration can be obtained by changing the transition s11, s10r, and so the next configuration the 1 to a 0, remaining in state s1 and moving to the right, so that we get the configuration 1 -0, s -1, 1, and we see from our turing machine that it contains the transition s -1 -1 -l, and this tells us the next configuration can be obtained by changing.
03:49
The 0 to a 1, changing to state s2, and moving to the left.
03:56
So we obtain 1s2 010.
04:12
And finally, we notice that none of the transitions begin with an s2, and so it follows that the machine halts at this stage, and therefore the final configuration of the tape reads 1 -010 from left to right.
04:36
My mistake.
04:49
I'm sorry.
04:50
The instructions in this problem gave me the wrong turing machine.
04:55
The turing machine should really contain the five tuffles.
04:59
S -0 -s -10 -r, s -1 -s -1 -0 -s -1 -l, s -0b, s -1 -1 -r, s -1 -1 -r, s -1 -1 -r, s -1b, s -1b, s -2 -0 -r, and s -1b, s -3 -0 -r.
05:23
So i'm going to redo this part.
05:30
This time we'll do it a little bit faster.
05:32
So we'll start off with our initial configuration, s -0.
05:41
I'll just write the transitions above on an arrow.
05:46
And so you see that machine contains the transition s00, s1, r.
06:02
So the new configuration, while we're going to keep the zero, we're going to move to the right and we're going to change to state s1, so it's 0 s1101.
06:15
And we see that the turing machine contains the transition s -1 -s -1 -r.
06:29
And so the next configuration can be obtained by keeping the 1 -1, moving to the right and remaining in state s -1.
06:39
So we now have 0 -1, s -1, s -1...
