## Difference Between NFA and DFA

**NFA vs DFA**

The theory of computation is a branch of computer science that deals with how problems are solved using algorithms. It has three branches, namely; the computational complexity theory, the computability theory, and the automaton theory.

The automaton or automata theory is the study of abstract mathematical machines or systems that can be used to solve computational problems. An automaton is made up of states and transitions, and as it sees a symbol or letter of input, it makes a transition to another state taking the current state and symbol as input.

The automaton or automata theory has several classes that include the Deterministic Finite Automata (DFA) and the Nondeterministic Finite Automata (NFA). These two classes are transition functions of automata or automaton.

In transition, DFA cannot use n empty string, and it can be understood as one machine. If the string ends at a state that is not an acceptable state, DFA will reject it. A DFA machine can be constructed with every input and output.

DFA only has one state transition for every symbol of the alphabet, and there is only one final state for its transition which means that for each character that is read, there is one corresponding state in DFA. It is easier to check membership in DFA but it is more difficult to construct. Backtracking is allowed in DFA, and it requires more space than NFA.

Backtracking is not always allowed in NFA. While it is possible in some cases, in others it is not. It is easier to construct NFA, and it also requires less space, but it is not possible to construct an NFA machine for every input and output.

It is understood as several tiny machines that compute simultaneously, and membership can be harder to check. It uses Empty String Transition, and there are numerous possible next states for each pair of state and input symbol. It starts at a specific state and reads the symbols, and the automaton then determines the next state which depends on the current input and other consequent events. At its accepting state, NFA accepts the string and rejects it otherwise.

Summary:

1.“DFA” stands for “Deterministic Finite Automata” while “NFA” stands for “Nondeterministic Finite Automata.”

2.Both are transition functions of automata. In DFA the next possible state is distinctly set while in NFA each pair of state and input symbol can have many possible next states.

3.NFA can use empty string transition while DFA cannot use empty string transition.

4.NFA is easier to construct while it is more difficult to construct DFA.

5.Backtracking is allowed in DFA while in NFA it may or may not be allowed.

6.DFA requires more space while NFA requires less space.

7.While DFA can be understood as one machine and a DFA machine can be constructed for every input and output, 8.NFA can be understood as several little machines that compute together, and there is no possibility of constructing an NFA machine for every input and output.

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NFA CONSUME MORE SPACE AND DFA REQUIRES LESS SPACE…..

right priyanka

You Both are wrong NFAs are often smaller than DFAs and hence consume less space.

Thanks neha.

And stifler you are wrong because in NFA transitions (inputs) and States are more than DFA. Hence NFA consume more space then DFA….

While DFA can be understood as one machine and a DFA machine can be constructed for every input and output, NFA can be understood as several little machines that compute together, and there is no possibility of constructing an NFA machine for every input and output. why?

thanks to priyanka for asking a question….

thanks to neha for answering a right answer….

stifler you are wrong….