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Difference between NFA and DFA with Comparison Chart

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Difference between NFA and DFA with Comparison Chart
Stechies

What is NFA and DFA? What is the difference between NFA and DFA? How are the features and functionality of DFA and NFA different from each other? These and other similar questions are being asked in interviews jobs requiring pre-knowledge of finite automata or finite automaton or theory. The finite automation theory necessitates the use of several classes with NFA and DFA being the most important of them all.

The main difference between DFA and NFA, the two classes handling the transition functions of finite automata/ finite automaton theory, impact their behaviour in many ways. In this article, we aim to explain the difference between DFA and NFA in tabular form to help users understand what is DFA and what is NFA in the simplest terms. Read on for more.

DFA Vs NFA

Given below is a comparison chart explaining DFA vs NFA in tabulated form on the basis of certain differences.

Basis of Difference

DFA

NFA

Reaction to symbols

For each symbolic representation of the alphabet, only a singular state transition can be attained in DFA.

No specifications are needed from the user with respect to how certain symbols impact the NFA.

Empty string transition

DFA is not capable of using Empty String transition.

Empty String transition can be used by NFA.

Structure

DA can be best described and understood as one machine.

NFA is in the nature of multiple small machines that are performing computational activities at the same time.

Rejection of string

DFA rejects the string in case it terminates in a state that is different from the accepting state.

NFA rejects the string in the event of all branches dying or rejecting the string.

Backtracking

It is possible to use backtracking in DFA.

It is not possible to use backtracking at all times in case of NFA.

Ease of construction

Given its complex nature, it is tougher to construct DFA.

NFA is more easily constructed in comparison to DFA.

Supremacy

All DFAs are derived from NFAs.

All NFAs are not DFAs.

Transition functions

The number related to the next state is one.

The number related to the next state/ states is either zero or one.

Complexities of time

The total time required for running any input string in DFA is less than what it is in NFA.

The total time required for running any input string in NFA is larger than that in comparison to DFA.

Full form

The full form of DFA is Deterministic Finite Automata.

The full form of NFA is Nondeterministic Finite Automata (NFA).

Space requirement

More space allocation needed.

Less space needed.

Setting of next possible set

The next possible state is clearly set in DFA.

In NFA, every individual pair of input symbol and state may contain many possible next states.

 

What is NFA?

NFA refers to Nondeterministic Finite Automaton. The term nondeterministic in NFA means that the NFA can exist in, or can make transition to, many different states at the same point of time for given inputs.

  • NFA can also be defined as a nondeterministic finite state machine. In NFA, the transitions are not uniquely determined by their input symbol or source state.
  • The reading of input symbols is not required for every individual state transition.
  • All DFAs are also NFAs

What is DFA?

DFA refers to Deterministic Finite Automaton. The term deterministic in DFA means that the DFA can exist in, or can make transition to, only one state at a given point of time for given inputs. It explains the uniqueness of the computation.

  • In the theory of computation, which is a branch of computer science (theoretical), DFA is also referred to as a deterministic finite accepter (DFA) or deterministic finite-state machine. Overall, it is a finite-state machine which has been designed to accept/reject only finite strings of symbols.
  • DFA will produce a unique computation/ run enabling the automaton of each input string.
  • DFA is an abstract mathematical concept. It is used in software and hardware for finding solutions to specific problems.
  • DFA recognizes regular languages for the purpose of performing lexical analysis, pattern matching, etc.
  • DFAs are designed from nondeterministic finite automata (NFAs) by incorporating the powerset construction method.

Key difference between DFA and NFA

The following points highlight some important differences of NFA vs DFA:

1.Deterministic Finite Automaton or DFA is a type of FA wherein only one path is possible for any specific input to transit from its current state to the next state. There exists a unique transition for each input symbol. On the other hand, Non-Deterministic Finite Automaton or NFA refers to a type of FA wherein in it is possible to have many paths for a given set of inputs to make their transition from their current state to the next states.

2.Empty String transition cannot be used in DFA. Conversely, NFA Empty String transition is possible in NFA.

3.A DFA is best explained in the form of one machine and not as separate units for computing purposes. NFA is a collection of multiple little-sized units that are combined together to perform computation activities.

4.DFAs reject the string in case the termination state is other than the accepting state. On the other hand, NFA rejects the string only when all branches of the NFA are dead or do not accept the string.

5.There is just one transition state for every alphabetic symbol. Conversely, no user-specifications are needed for making NFAs react in line to symbols.

Conclusion

The above paragraphs help you understand the difference in transition from DFA to NFA and NFA to DFA. The NFA DFA differences go deep and are very useful for enabling their correct usage in the finite automata/ finite automaton theory. In case you have any further inputs or queries with regards to DFA definition, NFA definition, difference between NFA and DFA, features of NFA and DFA, etc. then please get back to us in the Comments section below. Our team will help you sort out the needful immediately.


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