NFA vs DFA: Difference and Comparison

The full form of NFA is Finite Automata, and DFA means Deterministic Finite Automata. Both of these terms belong to the subject called Automata theory, as their names imply.

In simple language, automata theory tells us how a machine works, that is, what logical steps it follows to conclude a calculation it had been given to operate on. 

Thus, in this subject, both of the given terms, NFA and DFA, are models that help us know and map the functioning of the machine.

It is, however, important to note that both models help us understand simple models mostly, as mapping the operation of complex processes and algorithms is tough.

The main purpose of these models is to show the transition a process undergoes at each step. This means at each stage; there is an option of going to another state or staying in the current state in the next step. This is what the models show.

Key Takeaways

  1. NFAs have multiple possible transitions for a single input symbol, whereas DFAs have only one.
  2. DFAs can only move from one state to another on input symbols, while NFAs can also do so on empty strings.
  3. NFAs are less restrictive than DFAs, which makes them easier to design and understand, but harder to implement.

NFA vs. DFA

NFA is a term used in automata theory. NFA stands for Finite Automata and represents a transition diagram where multiple paths can be taken to move from one state to another. DFA stands for Deterministic Finite Automata. It also presents a transition diagram in which only one path can be taken to move from one state to another.

NFA vs DFA
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Comparison Table

Parameters of ComparisonNFADFA
DefinitionNFA is the transition diagram where there are more than one ways to go from one state to another.DFA is the transition diagram where there is one way to go from one state to another.
ExistenceNFA exists.DFA is a theoretical concept.
DerivationNFA is independent.DFA is a derivation of NFA.
Ease of ConstructionNFA is easy to construct.DFA is relatively difficult to construct.
Number of Next StatesA number of the next states are one.The number of next states can be zero, one, or more.

What is NFA?

The full form of NFA is Finite Automata. It is a concept in automata theory, first introduced in 1959 by Michael O. Rabin and Dana Scott. The basic working of an NFA is where a bunch of symbols are input, and the machine parses them individually.

For each symbol, the machine is in a particular state. On receiving a particular symbol, it moves to another state. When the symbols are exhausted, and no other symbol is left, the state in which the machine is present is noted.

There can be one or more predefined final states. If the actual final state corresponds with one of the predefined final states, then we say the language is compatible with that automata. We keep several things in mind in the case of Nondeterministic Finite Automata.

The important ones are that we have multiple ways of moving from one state to another in an NFA. The transitions can not be uniquely determined by their input symbols. Backtracking, however, may or may not be allowed.

Another very prominent feature of NFA is the existence of empty transitions. By an empty transition, we mean that the automata might not consume a symbol but still move from one state to another because of this empty state transition.

Nondeterministic Finite Automata are easier to construct and occupy very little space. But, despite having so many advantages of DFAs, NFAs consume more time to solve a similar operation than a DFA would take.

What is DFA?

DFA means Deterministic Finite Automata. Similar to NFA, it is also a term used in automata theory, which follows the same mechanism as Nondeterministic Finite Automata. It takes in a string of symbols and parses them one after the other.

There are predefined final states. If, after the completion of parsing, the final state reached is in the set of the predefined final state, then we say that the DFA accepts the string, else we say that it does not accept it. 

However, the most important thing to know is that DFA does not exist in reality, and is only a theoretical concept. DFA is derived from NFA; thus, all DFAs are NFAs, but all NFAs are not DFAs.

The most important characteristic of a DFA is that there is only one way to get from one state to another, and there exist no null state transitions, and while backtracking may or may not be allowed in an NFA, it is always present in a DFA.

Since there is a lack of null state transition and multiple state paths, it is obvious that there is a state transition corresponding to each input symbol.

DFAs are more difficult to construct due to the demand for a unique path and also occupy a lot of space. However, DFAs take much less time to resolve a problem than NFAs.

Main Differences Between NFA and DFA

  1. The main difference between NFA and DFA is that NFA has multiple state transition paths, while DFA has a unique state transition path.
  2. NFA is an actual concept, while DFA is just a theoretical concept.
  3. NFA is independent, while DFA is a derivation of NFA.
  4. NFA is easy to construct, while DFA is relatively difficult to construct.
  5. NFA takes more time to process a string, while DFA is faster.
References
  1. https://link.springer.com/chapter/10.1007/3-540-63174-7_12
  2. https://patents.google.com/patent/US9177253B2/en

Last Updated : 11 June, 2023

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