NFA to DFA

The language accept by finite automata:
The language accepted by a dfa M = (Q,?, ?, q0, F) is the set of all strings
on ? accepted by M. In formal notation,
L (M)= {w??* : ?* (q0, w)? F} .
The language L accepted by an nfa M = (Q,?, ?, q0,F) is defined as the
set of all strings accepted in the above sense. Formally,
L (M)= {w??* : ?* (q0, w)? F??} .
In words, the language consists of all strings w for which there is a walk
labeled w from the initial vertex of the transition graph to some final vertex.
Definition:
A language L is called regular if and only if there exists some deterministic finite accepter M such that
L = L ( M ) .
Construct an Equivalent DFA from NFA.
Two finite accepters Ml and M2 are said to be equivalent if
L(M1)=L (M 2)
that is, if they both accept the same language.
Every DFA is an NFA, it is clear that the class of languages accepted by NFA’s includes the languages accepted by DFA’s. This technique, called subset construction. To convert NFA to DFA carry out the following algorithm:
procedure: nfa-to dfa
L. create a graph GD with vertex {q0}. Identify this vertex as the initial vertex,
2. Repeat the following steps until no more edges are missing
Take any vertex {qi,qj, …, qk} of GD that has no outgoing edge for some a ?? .
Compute ?* (qi,a) , ? * (qj,a) ..., ? * (qk,a).
Then form the union of all these ? *, yielding the set {q1,qm,…,qn}
Create a vertex for GD labeled {q1,qm,…,qn} if it does not already exist.
Add to GD an edge from {qi,qj,...,qk} to {q1,qm,...,qn} and label it with a.