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Welcome to the class where I vendor bah blah blah so today I am going to discuss theory of computation TOC and before starting the class I would like to tell you a few points first of all this class is only about gate so I am NOT going to discuss all possible theorems all possible proofs and conjectures I will be discussing mainly about gate so the main intension of this class is to help you in answering all the gate questions so I will be mostly interested in discussing the techniques and maybe some important methods using which you will be able to answer all the gate questions I am NOT going to discuss all the proofs all the theorems all the conjectures that is the first important point and the second important point when you are watching this video if you don't understand anything you can stop it there go back and listen to the point again and come back to the next topic right and I will even give you some time to take down the notes even if I didn't give you any time to take down the notes you can just pause the video right to the important points or maybe take a detail notes and then continue and even if you don't understand some few problems when I'm teaching don't worry just go through the complete video maybe finish off the entire subject definitely you will understand everything by the end so if you don't understand anything at any point don't worry just finish off the video we shall know you can again if you the video and then you can understand it okay so let me start this subject today I am going to discuss TOC theory of computation daemons theory o means of seamless computation so by this name you must be understanding that this is something about of computation so what is computation computation is nothing but any tasks that can be performed by a calculator or a computer so we are going to mathematically model a computer or any machine in general and then we are going to study the theory about it which means what are the capabilities of this machine what are the problems that could be solved by this machine and what are the limitations of such a machine making so the basics of this subject are I am going to discuss all the basics now right first of all the basics of this symbol is the basic of the subject is a symbol what is a symbol symbol is the basic building block in this subject of TOC and a symbol can be any letter like this or anything even you can have picks this is a symbol from a symbol we can form alphabet this is generally represented by Sigma Sigma is also called as alphabet so the alphabet is nothing but some collection of these symbols for example a comma B now once if you define the alphabet all these strings okay what is the string I am going to discuss it everything will be based on this set predefined set called alphabet so you can this you can have any number of alphabet any number of symbols in the alphabet in this sense you can even have ABC or you can even have 0 1 or you can even have 0 1 2 9 it is a finite set and it can be anything okay and from the alphabet we are going to discuss a string a string is a sequence of the symbols which is nothing but example is let us say a if alphabet is a comma B small J is a string over this alphabet which is of length 1 and small B is also a string of alphabet which is of length 1 and a a is also a string of the alphabet which is of length 2 a B BC so on so maybe if you consider this alphabet some of the interesting questions are how many strings of length en are possible over this alphabet how many strings of length 2 are possible over this alphabet length 2 again so you can say a a a b b a b b which means for now i am asking you how many strings of length n or possible length n or possible we have n blank spaces and we have two options to fill in width right so what are the two options either A or B either A or B so on which means two into two into two into so on n times so which is 2 power n so in fact you can even extend this concept to any alphabet since we have only two symbols in this alphabet we have got 2 power n so in general if you have n symbols or let us say the number of signals in this Sigma if they are represented by mod Sigma then the number of strings of length n possible over Sigma is Sigma power M Sigma power n so just think about it just revise what we have seen till now first thing is symbol what is a symbol symbol is the smallest building block in Diversey and if you take few symbols we can form an alphabet once we have defined an alphabet we are going to form strings using only the symbols in that alphabet so symbol alphabet and string okay now using this I am going to define few more things next thing is language language what is the language so we know what is string is even if you consider english language english language is nothing but collection of words isn't it so in TOC a language is nothing but collection of strings isn't it so for example let us say Sigma equal to a comma B then languages can be defined like this language l1 equal to

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