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Thursday, November 23, 2023

Difference between DFA and NFA

In this article, we aim to explain the difference between DFA and NFA in tabular form to help users understand what DFA is and what is NFA in the simplest terms. Read on for more.

DFA vs NFA

NFA refers to Nondeterministic Finite Automaton. DFA refers to Deterministic Finite Automaton. DFA can be best described and understood as one machine. NFA is like multiple small machines that are performing computational activities at the same time. All DFAs are derived from NFAs. 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.

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 an Empty String transition. NFA can use an empty String transition.
Structure DFA can be best described and understood as one machine. NFA is like 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 refusing the string.
Backtracking It is possible to use backtracking in DFA. It is not possible to use backtracking at all times in the 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.
The setting of the next possible set The next possible state is clearly set in DFA. In NFA, every single pair of input symbols and states may contain many possible next states.

What is NFA?

NFA refers to Nondeterministic Finite Automaton. The term non-deterministic in NFA means that the NFA can exist in, or can make the 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 the 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 natural languages to perform 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

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

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