Difference Between NFA and DFA (with Table)

NFA stands for Nondeterministic Finite Automata and DFA stands for Deterministic Finite Automata. Both of these terms belong to the subject called Automata theory, as their names imply. In a simple language, automata theory tells us about how a machine works, that is, what logical steps does it follow to arrive at the conclusion of a calculation it had been given to operate on. 

Thus, in this subject, both of the given terms, NFA and DFA are actually models that help us know and map the functioning of the machine. It is however important to note that both of these models help us to 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.

The difference between NFA and DFA is that in an NFA there are many paths to go to another state from a particular state, however, in a DFA there is only one path to go to from a particular state.

Comparison Table Between NFA and DFA

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 actually 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 StatesNumber of next states is one.Number of next states can be zero, one, or more.

What is NFA?

NFA stands for Nondeterministic Finite Automata. It is a concept in automata theory, It was first introduced in 1959 by Michael O. Rabin and Dana Scott. The basic working of an NFA is where there are a bunch of symbols that are input and the machine then parses it one by one. 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 there is no other symbol left, then 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 that the language is compatible with that automata.

In the case of a Nondeterministic Finite Automata, there are several things that we keep in mind. The important ones are that in an NFA, we have multiple ways of moving from one state to another. 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 the existence 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 what a DFA would take.

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What is DFA?

DFA stands for Deterministic Finite Automata. Similar to NFA, it is also a term used in automata theory, which works by following pretty much the same mechanism as that of 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 string is accepted by the DFA, 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 actually derived from NFA, and 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 it occupies a lot of space too. However, DFAs take much less time to get done with a problem as compared to NFAs.

dfa graphical representation

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.

Conclusion

Understanding how the machines work is an important part of knowing how to build future technologies and how to custom-build machines and devices that are better suited for a particular job. It also helps us know what optimizations should we give to the software so that they can work more efficiently with the pre-existing hardware.

Even though DFA is just a conceptual term, it is important to understand, as based on that we are able to understand many other different kinds of NFAs, different than the kind we derived it from.

References

  1. https://link.springer.com/chapter/10.1007/3-540-63174-7_12
  2. https://patents.google.com/patent/US9177253B2/en