Nondeterministic Finite Automata

This is an example of what is called a nondeterministic finite automaton (NFA). Intuitvely, such a machine could have many possible computations on a given input. For example, on an input of the form u001v, it is possible for the machine to reach the accepting state qp by transitioning from q to q0 after reading u. Similarly, it is possible for the machine to reach qp also on the input u01v — for this to happen, the machine stays in q as it reads u, transitions to q0 on reading 0 after u, transitions to q00 without reading an input symbol by following the transition labeled , goes to qp on reading 1, and stays in qp while reading v. On the other hand, the machine also have other possible computations on both u001v and u01v — it may stay in q and never transition out of it; or it may transition to q00 on reading u0 by following the -transition from q0 and die attempting to take a transition labeled 0 (that doesn’t exist) out of q00. The fact that the machines behavior is not determined by the input string, is the reason these machines are called nondeterministic.