Log In
0 votes

 Every DFA is NFA but not vice versa

Can you please explain how this statement is true?


in Theory of Computation
edited by

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

0 votes
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

Related questions

0 votes
1 answer
When we convert a (minimal) NFA to DFA by subset construction method, is the DFA obtained always a minimal DFA? Please elaborate.
asked Nov 15, 2018 in Theory of Computation Mizuki 165 views
0 votes
1 answer
3 votes
1 answer
According to this Hopcroft's algorithm , we can efficiently minimize a Finite automata in $O(nlogn)$ time (polynomial time algo) then why it is said that Minimizing Finite Automata is computationally hard according to this link ?
asked Mar 27, 2018 in Theory of Computation ankitgupta.1729 442 views