<Li> Keep a set data structure of all states which the NFA might currently be in . On the consumption of an input symbol, unite the results of the transition function applied to all current states to get the set of next states; if ε - moves are allowed, include all states reachable by such a move (ε - closure). Each step requires at most s computations, where s is the number of states of the NFA . On the consumption of the last input symbol, if one of the current states is a final state, the machine accepts the string . A string of length n can be processed in time O (ns), and space O (s). </Li> <Li> Create multiple copies . For each n way decision, the NFA creates up to n − 1 (\ displaystyle n - 1) copies of the machine . Each will enter a separate state . If, upon consuming the last input symbol, at least one copy of the NFA is in the accepting state, the NFA will accept . (This, too, requires linear storage with respect to the number of NFA states, as there can be one machine for every NFA state .) </Li> <Li> Explicitly propagate tokens through the transition structure of the NFA and match whenever a token reaches the final state . This is sometimes useful when the NFA should encode additional context about the events that triggered the transition . (For an implementation that uses this technique to keep track of object references have a look at Tracematches .) </Li> <P> NFAs and DFAs are equivalent in that if a language is recognized by an NFA, it is also recognized by a DFA and vice versa . The establishment of such equivalence is important and useful . It is useful because constructing an NFA to recognize a given language is sometimes much easier than constructing a DFA for that language . It is important because NFAs can be used to reduce the complexity of the mathematical work required to establish many important properties in the theory of computation . For example, it is much easier to prove closure properties of regular languages using NFAs than DFAs . </P>

There are languages accepted by dfa's which cannot be accepted by nfa's