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 Every DFA is NFA but not vice versa

Can you please explain how this statement is true?


in Theory of Computation by Junior (883 points)
edited by | 160 views

From the link you gave

NFA is similar to DFA except following additional features:
1. Null (or ε) move is allowed i.e., it can move forward without reading symbols.
2. Ability to transit to any number of states for a particular input.

These are the additional benefits that NFA gives but it is not always compulsory to use them. If we don't use them then it becomes just like DFA.

But if we use these added features we can't say it is a DFA.

So we can say that NFAs can act like DFAs as well as like something more than DFAs. In this context you can think like DFA as a proper subset of NFA. 

Then " Every DFA is NFA but not vice versa" is true.



You can take analogy between an international airport(DFA) and a domestic airport(NFA). Every international airport(DFA) can be considered a domestic airport(NFA) in a way because domestic flights fly from there anyway. But every domestic airport(NFA) cannot be considered as international airport(DFA).

However unlike the analogy of airports, DFA and NFA are equivalent in power since they can be converted to each other.

1 Answer

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Generally DFA From every state on every input symbol exactly one transmission exists

Where as in Nfa More than one or none transmission exists

But Expressive powers are same
by (447 points)
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