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Add initial acceptor

in the previous lecture we have seen the formal definition of Turing machine and in this lecture we will be seeing an example of Turing machine and we will see how we can design a Turing machine for a given language all right so here we have a question which says design a Turing machine which recognizes the language L equal to 0 1 star 0 now what is this language means this language means it should have 1 0 followed by any number of ones followed by 1 0 at the end so if you see that this language is a regular language we might have taken this example even in our previous lectures and you must be knowing that this is a regular language and we actually can design this language using a finite state machine because this is a regular language but we are going to do it using Turing machine so that we can understand step-by-step from the very simplest example of how to design a Turing machine we don't actually need the full power of Turing machine in order to design this language this can also be done using a finite state machine or a pushdown automata but we are going to design it using the Turing machine to show you how it actually works from the very basic or from the very simplest steps all right so let's see how the Turing machine for this can be designed so here we have the Turing machine for the language that we have to design which is L equal to 0 1 star 0 so here we have the starting state which is a and then we have two states B and C and then we have two final States which are the reject state and the accept state and let us see how it works so as we want to accept 0 1 star 0 in the initial state or the starting state when we get a 0 we go to the next state B and then in our tape we write the symbol X and we move right on our tape and we come to state B and we know that we have to except any number of ones after we accepted this zero so in state B if you get any number of ones you always stay in state B and then in our tape you write the symbol Y and then you move right on the tape and after getting any number of ones finally we need to get a zero so if you get a zero what you do you proceed to the next state which is state C and then you write X on the tape and then you move right on the tape and after we reach the state C we see that there is nothing more to take so what we do we read the blank symbol that means we read something that is empty or the blank and if we see the blank symbol what we do we don't write any other symbol other than the blank symbol into the tape and then we move right on the tape and it goes to the accept state so this is how it works so let us just take an example and see how this works using the tape so let's say that we are going to take this string 0 1 1 0 so we see that there is 0 and then we are allowed to take any number of ones so we have 2 ones here and we have a 0 at the end so this should be accepted by this tutoring machine so first of all we come to the tape and my tape head is over here in the beginning and then if you get 0 what happens we write X on our tape so in my tape let me write X and then you go to state B and you move right on the tape that means my tape head comes over here now all right and now the next input we have already read 0 and the next input that we have is 1 now if we get 1 what happens we are in state B and in state B if we get 1 we stay in B itself and we write Y onto our tape so this is my tape head so here I write Y and then what we do we move right on the tape so my tape here which was here will now move to the right which is one step right all right and then the next input that we have is another one so we are still in state B and if you get another one what you do you stay in state B and you write Y on the tape and then you move right so my tape head is over here I write Y over here and then my tape head will move one step to the right which is over here okay and then the next input that I have is a 0 so in B if you get a 0 what happens it goes to state C and then we write x on our tape and we move one step right so I will write x on my tape my tape it is over here so just below that I write X and then we have to move one step right this right over here so I move one step right and now we see that we have reached the end of the string so here there is nothing and we consider this to be the blank symbol so we are in state C and when we read the blank symbol what happens we write blank on the tape and we moved one step to the right and we go to the except state so here is my tape head I will write the blank symbol and I will move my tape head one step to the right okay so this is the condition of my tape now and then I have reached the except state so since we have reached the except state this string will be accepted so this is how the strings will be accepted or recognized by the Turing machine now there is one question that you can ask why are we writing these symbols X Y Y X on the tape so as I told you in the beginning this is a very simple language it is a regular language and you actually do not need the full power of a Turing machine in order to implement this but we have to do this because we are using the Turing machine and particularly for this language this tape symbols don't have any particular use they are not of any particular use for accepting this language but we are just doing this in order to show you how to ring machine works and how the tape actually works so you don't actually need the tape but we have to use the tape because it is a 2 machine and another thing that you need to know is that in the first lecture itself I told you that Turing machines they are deterministic so deterministic means what when you draw the transition diagram there should be a transition for each and every input symbol that we have for each and every state so let's see if this is deterministic or not here we have state a and then in this language the input symbols that we have they are 0 and 1 and the special symbol that we have which is the blank symbol that is this one so we need to have transition for the symbols 0 and 1 which is the input symbols and we should also have transition for the blank symbol so remember that blank is not an input symbol but it is a special symbol and we need to have transition even for this so in state a we see that on 0 it goes to B and on 1 it goes to reject and on the blank also it goes to reject so for all the 3 it is having transitions and even in B in 0 it goes to C in 1 it goes to B itself and on the blank it goes to the reject state so even in C we see that for both 0 and 1 it goes to the reject state and on blank it goes to the accept state so we see that for each and every symbols input symbols including the blank symbol there is a transition for all the states that we have and we see how the student machine was working that is for 0 followed by any number of ones followed by 0 it comes to the accept state so in all other cases like if you are getting 1 in the beginning or blank in the beginning it goes to the reject and after getting a 0 in the beginning if you are getting a blank then it is going to the reject state and also in C after getting this 0 which is this final 0 over here and after this instead of getting a blank if you are going to get 1 or 0 it would also go to the reject State so this is how the student mission works and another thing you need to remember about the Turing machine is that sometimes when we draw the during machine you may notice that some edges may be missing so if some edges may be missing then you should understand that that edge by default it leads to the reject state so when we draw the stirring machine in some examples that I take if you don't see an edge but if you don't see a transition for a particular input don't think that it is wrong because I already told you it is deterministic and thinking that it is deterministic and if you are not seeing an edge you may sometimes think that it is wrong so don't think it is wrong but just know that if an edge is missing it goes to the reject state by default so here we have transition for all inputs on all the states and we have two final States which is the accept state and the reject state and unlike finite state machines where in the final state also we need to have transition for the inputs if it is a deterministic finite automata but in this one we don't give transition for the accept state and reject state they are two states that are either used for accepting or rejecting so it is deterministic and we saw how the tape is working and we also saw the important things that you should remember about the Turing machine so this was just a simple example to help you understand so on the next lecture onwards we will be taking more examples where we will be discussing more complicated languages that cannot be designed using the lower versions that we have discussed and can be designed using the Turing machine so I hope this lecture was clear to you thank you for watching and see you in the next one [Applause] [Music] you [Music]