 Hello student, welcome to the session on how to draw NFA with a null transition using Cleans Theorem Part 1, myself Rashmi Dixit. Learning outcome at the end of this session students will be able to draw non-deterministic finite automata machine with null transition. As we have already seen finite automata can be characterized into deterministic finite automata and non-deterministic finite automata. Third machine that is non-deterministic finite automata with null transition is a five tuple machine where q indicate a finite set of states, alphabets a finite set of input symbol, q0 the initial or starting state, f a set of final or accepting states which is a subset of q and a transition function where machine in any state by processing a single symbol or null machine may move to 2 raise to q where 2 raise to q is the power set of q the set of all subsets of q. In DFA there is exact one transition for each and every symbol that is machine in any state q by processing a single symbol machine move to another q or remain in the same state. In NFA machine in any state by processing a single symbol at a time machine may move to 2 raise to q where 2 raise to q is the power set of q. In addition to an alphabets here a null symbol means without processing anything machine may move to 2 raise to q the set of all subsets of q. The main problem or the main question here we are discussing how to draw NFA with a null transition. DFA we draw by checking each and every time whether a particular string is accepted at final state or not. In NFA with a null transition without processing anything machine may move from one state to another. So, how many states we can include in such a way? So these are the NFA with a null transition basic primitives. So the first diagram indicate machine with empty set, the second diagram indicate machine accepting null string, the third diagram is for machine accepting symbol a. How to draw NFA with a null transition? There are some rules which are defined by claims. So three different rule for three types of operation one is union, one is concatenation and one is cling star. Remember one thing DFA, NFA and NFA with a null transition all these three machines accept same type of regular language. While drawing NFA with null transition we will see each and every regular expression as a part of union concatenation or cling star and we will draw step by step operation by operation. So the rule one for union while drawing a diagram or a machine for union we will add new extra state as a initial state and this initial state will join with these two machine using null transition and all accepting states of the original machine will remain as it is. In concatenation the first initial state will be the initial state of first machine accepting state of the first machine will be connected to the initial state of the next machine with a null transition and all the accepting state of the second machine will remain as it is. So in concatenation we concatenate one machine after another one by connecting the accepting of the last to the initial of the next. In cling star we will add new extra state that will be connected to the initial state with null transition all accepting state will be connected to the new initial state with null transition and initial state also act as accepting state. We will see some examples so the picture will be clear. Now this is the first diagram for A plus B. So this is a machine for A plus B NFA with a null transition. So A B new state is added as a initial state which is connected with a null transition to the initial state of the original A and B machine respectively all the accepting state of the machine A and B will work as accepting state of our NFA with a null transition. Now this is a diagram of A B concatenation. So machine A accepting state will be connected to the initial state of machine B initial state of machine A will remain as initial state of machine A B and final state of machine B will be the only final state of the machine A B. Now A star for A star we will add one step or one stage as a initial stage and final state will be connected to the initial stage with a null transition initial state also act as final state. We will see one example so consider a regular expression 0 0 plus 1 bracket star followed by 1 0 bracket star. So let us draw the diagram step by step remember one thing we will consider regular expression part by part so we will start from the basic machines. So this is a machine accepting 0 initial state final state this is a machine accepting 1. Now try to draw the machine accepting 0 0 so concatenation. So final state of 0 will be connected to the initial state of 0 only the final state of second 0 will remain as a final state. Machine accepting 1 0 final state of 1 will be connected to the initial state of 0. So final state of 0 will only remain as a final state. Now next is 0 0 plus 1 so 0 0 plus 1 extra state is added as a initial state which is connected to the original initial state with a null transition and both accepting state will remain as it is. So next is 0 0 plus 1 star so new state which is connected with the final state with a null transition and initial state is also act as a accepting state all other accepting state is cancelled. Now the next part is 1 0 so 1 0 star so new state with a null transition connected to the initial that new initial state act as a accepting state which is connected from the original accepting state with a null transition. Now 0 0 plus 1 star 1 0 star so look at here we connect 2 separate machines that is 1 machine is 0 0 plus 1 star we will connect with a concatenate with a 1 0 star. So the final state of the first machine will be connected to the initial state of the second machine with a null transition only the accepting state of the second machine will remain as accepting state so this is a accepting state of the complete picture. In case of clean star initial and accepting stage are same so here from the initial state we connected to the next sorry final state we connected to the initial state of the next. So all the student please pause the video and try to draw the diagram for this particular regular expression part by part first 0 plus 1 then 0 plus 1 star then 1 0 then separate 0 0 star which will be concatenate with 1 1 star both these machines will be united and then clean star hope you are able to draw check with me so your answer is same as mine if some changes make the changes so this is a reference thank you.