 that is extended transition function for non-deterministic finite automata with null transition. Myself Rashmi Dixit, so let us begin the session, learning outcome at the end of this session students will be able to describe extended transition function for NFA with null transition. They are able to find whether a particular string is accepted by NFA with null transition. As we have already seen finite automaton can be grouped or characterized into two types of machine. The one is deterministic finite automata where there is exact one path for each and every transition and non-deterministic finite automata there may be zero or more than one transition. DFA or NFA both accept the same type of regular language. Now the third machine is non-deterministic finite automata with null transition is a somewhat extension to non-deterministic finite automata with null symbol. Machine process sorry machine transit from one state to another without processing anything or by processing a null string. NFA with a null transition is a five tuple machine where q indicate a finite set of states, alphabet a finite set of input symbol q0 the initial or a starting state, f a set of final or accepting states which is a subset of q a transition function indicated by delta. Delta is defined as machine in any state by processing a single symbol or null. Machine move from machine move to one or more state that is 2 raise to q 2 raise to q is the power set of q the set of all subsets of q. See the difference here in DFA, NFA and NFA with null transition in DFA machine in any state by processing a single symbol machine either remains in the same state or move to the next state. In NFA machine in any state by processing a single symbol machine move to 2 raise to q same as NFA 2 raise to q is the power set of q but in NFA with null transition machine in any state by processing a single symbol or null here the movement also present from one state to another without processing anything or by processing a null string that is a main characteristic of non-deterministic finite automata with null transition. So, in the last video session we have already seen what is null closure set of a state and that null closure set we required in extended transition function that is delta star. As we have seen in DFA or NFA extended transition function represent where the machine end after processing a complete string same as for NFA with null transition where the machine end after processing a complete string but here machine state move from one state to another without processing anything. So, let us see the recursive definition let m with a phi tuple q alphabet initial state set of accepting state and transition is an NFA with null transition the extended transition function which is indicated by delta star is represented as machine in any state by processing a complete string where the machine move that is 2 raise to q is defined as follow for every q or state which belongs to q extended transition function from q for null is null closure of that particular state for every q which belongs to q now y is a string and a is a symbol. So, extended transition function for a string is null closure of that is by combining a result set which is which we will get after processing a complete string except last symbol that is delta p, a where p will take the value of extended transition function from q to the complete string y a string x is accepted by machine if delta star q, x intersection a is equal to phi. So, let us we will solve one problem so that you will get a clear idea of how to check whether a particular string is accepted by machine or not. Let us see this diagram where q is the initial state w is the accepting state now see here from q by processing a null machine move to p, t same as s from s without processing anything moves to w from w to q 0 from q 0 to p, t that also that we we have seen in the last video. So, now we will solve the one problem for extended transition function now I want to check whether that is a is accepted by machine or not. So, by formula delta star q, a is a null closure of union delta p, a where p will take the value of delta star q 0 comma null by definition we know that is delta star q 0 comma null is null closure of q 0 machine remains in the same state after processing null, but as it is NFA with a null transition so null closure of q 0 so we will start from q 0 so from q 0 without processing anything machine move to p and t so null closure of q 0 is q 0 comma p comma t from p and from t there is a null transition so the answer is null closure of q 0 is q 0 comma p comma t now this is the answer of this particular p and this answer will be here so we will combining delta q 0 comma a union delta p comma a union delta t comma a so from q 0 there is a null transition from p there is a transition of a and machine remains in the same state so p from t there is a transition to u so phi p u now time to find null closure of p and u so from p there is a null transition from u also there is a null null transition so delta star q comma a is p comma u let us see one more example that is delta star q 0 comma a a so we will break last symbol that is delta p comma a p will take the value delta star q 0 comma a so delta star q 0 comma a is p and u so we will process p comma a union delta u comma a so null closure of p comma phi so null closure of p is p now all the student please pause the video and find try to find out the answer for delta star 1 comma a here a transition table with save for NFA with a null machine is given the machine has seven states a b and null symbol processing is mentioned in the column so try to find out delta star 1 comma a hope you solve this check with me so delta star 1 comma a so by processing null from a machine remains in the same state with null so null closure of 1 so null closure of 1 1 will be by default so from 1 by processing null machine move to 2 so 2 into our set from 2 by processing null machine move to phi u so phi u from phi u there is a no null transition so stop so null closure of 1 is 1 to phi u now next is we want to find out what that is delta star 1 comma a so by definition we are combining all the result state which we will get before processing delta p comma a p will take the value delta star 1 common null we know the value of delta star 1 common null that is 1 to phi u and now we will process a on each state in our answer state so delta 1 comma a union delta 2 comma a union delta phi u comma a so null closure of phi 3 and phi so null closure of 3 is 3 only so answer is 3 this is a reference thank you