 Welcome to the next session on conversion of a non-deterministic finite automaton to deterministic finite automaton that is NFA to DFA using subset construction method, myself Rashmi Dixit. So let us begin the session at the start, learning outcome. At the end of this session students will be able to solve problems for conversion of a particular NFA to DFA using subset construction method. As we have already seen what is deterministic finite automaton. So it is one type of finite automaton in which for every string x there is a unique path from initial state. X is accepted if and only if this path ends at final state. Non-deterministic finite automaton for any string x there may exist 0 or more than one path from initial state. Multiple transitions on the same input symbol or no transition on an input symbol these are the main reasons of non-determinism. To convert NFAs to DFAs we needed to get rid of non-determinism from NFAs. Actually DFAs and NFAs both are equivalent. DFAs are clearly a subset of NFAs. For a particular language if we draw NFA it is possible to convert into DFA which accept the same regular language. Any NFA can be converted into a DFA by simulating sets of simultaneous states. Why non-determinism exists? For the combination of state and input symbol there may result into more than one state. Each DFA state corresponds to a set of NFA states. While converting NFA to DFA there are some steps or algorithm before that we will see how our DFA will be. Given a NFAM where Q alphabet transition initial state and set of accepting state we are going to build a DFA M dash where Q dash contain all subset of states in Q. The initial state of M dash is the set of containing Q0 F dash is the set of all subsets of Q that contain at least one element in F. Equivalently the subset contains at least one final state. Now delta dash that is transition corresponding to the state S and the input symbol A which is indicated by this particular equation or formula where delta dash S of A is equal to union of delta P of A where P belongs to S. There is exactly one state that result the union of all sets delta P of A. We are going to remove unreachable states in Q dash. Subset construction method is the primary or the main method used for converting a given NFA to DFA. The following are the steps. For every state in the NFA we are going to determine all reachable states for every input symbol. The set of reachable state constitute a single state in the converted DFA. Each state in the DFA corresponds to a subset of states in the NFA. We are going to find reachable states for each new DFA state until no more new states can be found. We will see one example. So you will get the idea of conversion from given NFA to DFA. Now this NFA consists of four states Q0, Q1, Q2, Q3 where Q0 is initial state, Q3 is final or accepting state and symbols are 0 and 1. Now we will start solving one by one. Always start with the initial state. So delta dash Q0, 0, answer is Q0 that is pi processing 0 from state Q0 machine remains in the same state. Same way we process for one that is delta dash Q0, 1 by processing 1 machine remains in the same state as well as move to the Q1 so answer is set Q0, Q1. Q0 which is the initial state in the original given NFA also act as initial state in the converted DFA. We will only process those states which are reachable. So now time to process state Q0, Q1. We are simulating states into a single state. So delta dash Q0, Q1, 0 that is we are processing 0 on Q0, Q1. Now look at here we can union we are going to take the union of delta Q0, 0 and delta Q1, 0. So the final answer is Q0, Q2 that is delta dash Q0, Q1 for processing 0 gives us Q0, Q2. Same way delta dash Q0, Q1, 4, 1 delta Q0, 1 union delta Q1, 1. So the new state is Q0, Q1, Q2. Same way we make an entry into the table from Q0 the next state is Q0, Q1. Now time to process the next state which is generated that is Q0, Q2 delta dash Q0, Q2, 0 is delta Q0, 0 union delta Q2, 0. So from Q0, 4, 0 machine remains in the same state and from Q2, 4, 0 machine move to Q3. So the answer is Q0, Q3 delta dash Q0, Q2, comma 1 that is a processing of 1 at a state Q0, Q2 delta Q0, comma 1 union delta Q2, comma 1. So the new state generated is Q0, Q1, Q3. Now time to process delta Q0, Q1, Q2, 4, 0 and 4, 1. So after processing 0 it gives us new state that is Q0, Q2, Q3 and delta dash Q0, Q1, Q2, 4, 1 delta Q0, comma 1 union delta Q1, comma 1 union delta Q2, comma 1. And the answer is Q0, Q1, Q2, Q3. We are simulating states into single state. So entry into table continue. So 4 states are generated or reachable Q0, Q0, Q1, Q0, Q2, Q0, Q1, Q2. Now the next processing is delta dash Q0, Q1, Q3, 4, 0 delta Q0, 0 union delta Q1, 0 union delta Q3, 0. So the generated state is Q0, Q2. Same way delta dash Q0, Q1, Q3, comma 1, delta Q0, comma 1 union delta Q1, comma 1 union delta Q3, comma 1. So from Q1, sorry from Q0 there is processing of 1 and the generated states are Q0, Q1. From Q1 by after processing 1 machine goes to Q2. So union Q2 and from Q3 there is a no transition for 1. So the 5. So the state is Q0, Q1, Q2. Now time to process Q0, Q3, 4, 0 and 1. So delta dash Q0, Q3, comma 0 delta Q0, comma 0 union delta Q3, comma 0. So the state is Q0, delta dash Q0, Q3, comma 1 delta Q0, comma 1 union delta Q3, comma 1. So the generated state is Q0, Q1. So our table continue Q0, Q0, Q1, Q0, Q2, Q0, Q1, Q2, Q0, Q1, Q3 and Q0, Q3. Now remaining delta dash Q0, Q2, Q3, 4, 0 and delta dash Q0, Q2, Q3, 4, 1. So after processing 0 from Q0, Q2, Q3 the transition goes to Q0, Q1, Q3 and from Q0, Q2, Q3 after processing 1 transition goes to Q0, Q1, Q2. Remember one thing we will only check or process states which are reachable no need to process step wise. Now the next is delta dash Q0, Q1, Q2, Q3, 4, 0, 1. So the generated or the reachable states are Q0, Q1, Q2, Q3, 4, 0 from Q0, Q2, Q3, Q0, Q1, Q2, Q3 that is machine remains in the same state and Q0, Q2, Q3 after processing 1 from the state Q0, Q1, Q2, Q3. So the complete table here of a DFA so Q0 initial state and one important thing wherever Q3 that is accepting state of NFA is present in the simulating state that all becomes the accepting state of your converted DFA. Just look at the diagram. Now all students please pause the video and solve the given problem to convert the given NFA to DFA. Hope you solve answer is same. So this is a