Difference Between DFA and NFA
NFA denotes Nondeterministic Finite Automaton, and DFA stands for Deterministic Finite Automaton. DFA is best explained and understood as a single machine. NFA is analogous to several little machines simultaneously completing computing tasks. All DFAs are developed from NFAs. The main difference between NFA and DFA, the two classes that manage the transition functions of finite automata/finite automaton theory, has many effects on their behavior.
This article aims to describe the difference between the DFA and the NFA in a tabular format to assist readers grasp what the DFA and the NFA are. Continue reading to learn more.
What is DFA?
The acronym DFA stands for Deterministic Finite Automaton. It is said that a Finite Automata (FA) is deterministic if, for each input symbol, there is a single output state, i.e., just one transition. A finite deterministic automaton consists of five tuples expressed as,
Where,
Q: A non-empty finite set of states in the finite control(qo, q1, q2, …).
?: A non-empty finite set of input symbols.
?: It is a transition function that takes two arguments, a state, and an input symbol, and it returns a single state.
qo: It is the starting state, one of the states in Q.
F: It is a non-empty set of final states/ accepting states from the set belonging to Q.
Features:
- There is only one route from the current state to the next state for a specific input in DFA.
- DFA does not accept the null move, i.e., the DFA cannot change state if no input character is provided.
- DFA may include many final states.
Advantages:
- DFAs are one of the most applicable models of computing since it is simple to simulate a DFA on a stream of input using a linear-time, constant-space, online algorithm.
- Additionally, there exist efficient methods for identifying a DFA.
- The complement of the language that a particular DFA recognizes.
Disadvantages:
- No DFA can recognize the Dyck language because DFAs cannot count.
- A DFA-like automaton requires an endless number of states to represent any number of "now open" parentheses.
What is NFA?
NFA denotes Nondeterministic Finite Automaton. It is argued that a Finite Automata (FA) is non-deterministic if there are several alternative transitions from one state to the next for the same input symbol.
A non-deterministic finite automaton is alternatively expressed as a collection of five tuples.
Where,
Q: A set of non empty finite states.
?: A set of non-empty finite input symbols.
?: It is a transition function that takes a state from Q and an input symbol from and returns a subset of Q.
qo: Initial state of NFA and member of Q.
F: A non-empty set of final states and member of Q.
Features:
- Vertices are used to depict the state.
- The arcs that are designated with input characters indicate transitions.
- An arrow indicates the original condition.
- The double circle denotes the final state.
Advantages:
- Using NFAs, you may create an FA expressing a language that is the union, intersection, conflation, etc., of two (or more) languages.
- NFAs make it simpler for users to communicate their desires since they may pick from various paths.
Disadvantages:
- NFA often needs fewer states to understand the same language as DFA.
- Because the value of NFA lies in its capacity to access several subsets of its state set, NFAs with a one-letter input alphabet are more limited, and the gap between NFAs and DFAs narrows.
DFA vs. NFA
| DFA |
NFA |
- DFA stands for Deterministic Finite Automata.
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- NFA stands for Nondeterministic Finite Automata.
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- For each symbolic representation of the alphabet, there is only one state transition in DFA.
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- No need to specify how does the NFA react according to some symbol.
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- DFA cannot use Empty String transition.
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- NFA can use Empty String transition.
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- DFA can be understood as one machine.
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- NFA can be understood as multiple little machines computing at the same time.
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- In DFA, the next possible state is distinctly set.
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- In NFA, each pair of state and input symbol can have many possible next states.
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- DFA is more difficult to construct.
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- NFA is easier to construct.
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- DFA rejects the string in case it terminates in a state that is different from the accepting state.
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- NFA rejects the string in the event of all branches dying or refusing the string.
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Conclusion
Finally, we have come to the end of this detailed comparison between DFA vs. NFA. We hope you like this tutorial. We have started with a brief introduction to DFA and NFA. We also explored the advantages, disadvantages, and features of DFA vs. NFA. Finally, we have compared DFA vs. NFA.
Please let us know in the comment box if you have difficulty following along. Happy learning!
Related Questions
1. Are NFA and DFA equal?
Every DFA has an equivalent NFA. (Proof by construction - trivial.) Given N = (Q,?, ?, q0,F), NFA recognizes some language A. We prove that every NFA has an equivalent DFA by showing how to construct a DFA N from N that recognizes the same language A.
2. Why every NFA is not DFA?
Each NFA is not identical to the DFA, but each NFA may be translated into the DFA. NFA is defined in the same manner as DFA, except that it includes numerous subsequent states and transitions.
3. Can a DFA have no states?
Yes Possible. If an automaton is not an acceptor but a transducer, there is no requirement for a final state. Any kind of automaton may be devoid of a final state!
4. Can NFA have no final state?
Any NFA without accepting states is trivially identical to a DFA with two states: an initial, non-accepting state that loops to itself on all inputs, and an unreachable accepting state that loops to itself on all inputs.
