(00:01) Hello, everyone (00:02) Welcome to the next lecture (00:04) In the course and theory of Atom meta (00:06) In this lecture we will discuss about the formal definition of a Turing machine (00:12) In the previous lecture we studied about the the introduction of a Turing machine, (00:17) and now we will see how can we formally define a Turing machine? (00:21) All right (00:23) So Turing machine can be defined (00:27) as set of seven tuples, which are Q, Sigma, Tau, Delta, Q, Naught, B, and F (00:37) Now let us see what these tuples are (00:42) The first one is Q, which is the known empty set of stats (00:47) So you already know that also in finite state machine and pushdown Automata, (00:53) this Q tuple is used to represent the non empty set of States (00:58) And then we have Sigma and Sigma (01:00) Also, just like in other machines, it represents the non empty set of symbols (01:05) Or we can say it is the set of input (01:08) symbols that we have in our Turing machine (01:11) Then we have Tau (01:13) Now Tau is something different from finite (01:16) state machine and pushdown Automata, and it is the nonimplice set of tape symbols (01:22) When we studied the introduction of Turing machine, we saw that Turing machine has (01:27) something known as tape, and what is a tape? (01:31) It is an infinite sequence of symbols (01:33) So these symbols are the tape symbols (01:36) They are represented by this tuple Tau (01:39) So it is non empty set of tape symbols (01:43) And then we have Delta, which is the transition function (01:48) And we know that transition functions are (01:51) also there in finite Automata and push down Automata, and they are defined (01:56) in different ways according to how the machine works (02:00) So in case of Turing machine, (02:02) the transition function is defined as Q (02:05) cross Sigma, two Tau, cross R, R cross Q (02:13) Now let us see what this actually means (02:16) We know that in Turing machine we have (02:19) States and we have input symbols, and then we also have the tape symbols (02:25) So here this transition function means that if we are in a particular state (02:30) and we get a particular input symbol, then we write something into the tape (02:35) sequence and we move either right or left on the tape (02:40) And then we go to the next step (02:43) So this is what we mean by the transition function Delta in a Turing machine (02:49) This will be more clear to you when we (02:51) will take our examples in the next lecture, (02:54) and then we have Q naught, which is the initial state (02:58) Also, we have B, which is a plank symbol (03:02) So in introduction to Turing machine, (03:04) I told you that in the tab we have a special symbol card blank symbol, (03:10) which is used to fill the empty cells of a Turing machine (03:14) Also, this empty symbol does not belong to the set of symbols Sigma, (03:20) and then we have F, which is the set of final States (03:25) So also in introduction, I told you that there are two kinds (03:29) of final States in Turing machine that is accepted and reject state (03:35) So these are the seven tuples that are used to define a Turing machine (03:40) Now let us discuss the production rule of a Turing machine (03:47) Thus, the production rule of Turing machine will be written as (03:52) the input argument, which have two arguments Q naught and A, (03:59) and then the output have three arguments Q one, Y and R (04:05) So what does this mean? (04:07) This means that if we are in the initial state Q naught, and if we get input symbol (04:13) A, then we go to another state Q one, and we write the input symbol Y onto our (04:20) tab and we move to the right or left on our table (04:24) Here it shows that we move to the right (04:29) So it was all about the formal definition of a Turing machine (04:34) In the next lecture, we will take two examples (04:38) where we will construct Turing machines (04:40) for languages which we will discuss in the example (04:46) So thank you for watching and see you in the next lecture  ... in Turing machine that is accepted and reject state (03:35) So these are the seven tuples that are used to define a Turing machine (03:40) Now let us discuss the production rule of a Turing machine. .. in introduction to Turing machine, (03:04) I told you that in the tab we have a special symbol card blank symbol, (03:10) which is used to fill the empty cells of a Turing machine (03:14) Also,... the nonimplice set of tape symbols (01:22) When we studied the introduction of Turing machine, we saw that Turing machine has (01:27) something known as tape, and what is a tape? (01:31) It is