There are two ways of looking at a DFA. Some folks insist that every state must have a transition for every symbol in the alphabet (the transition function is a total function). If you look at a DFA this way, then, yes, as according to the accepted answer there will always be a cycle .
How would you describe DFA?
In DFA, for each input symbol, one can determine the state to which the machine will move . Hence, it is called Deterministic Automaton. As it has a finite number of states, the machine is called Deterministic Finite Machine or Deterministic Finite Automaton.
What is the difference between DFA and NFA?
| SR.NO. DFA NFA | 9 All DFA are NFA. Not all NFA are DFA. | 10 DFA requires more space. NFA requires less space then DFA. |
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Can a DFA have infinite states?
The language accepted by a DFA M with n states is infinite if and only if M accepts a string of length k, where n≤k<2n .
Can a DFA have no final states?
Yes Possible . If an automata is not acceptor but transducer then final state is not needed. Any class of an automata can be without a final state!
Can a DFA have one state?
can i not just have one state (initial and final state) that loops a,b to itself? Sure you can . What makes you think that it would be a problem? I suggest you write down formally the components of such a DFA, and see that they all fit the definitions.
Is DFA and DFSM same?
In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM) , or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of ...
What is the use of DFA?
DFA uses include protocol analysis, text parsing, video game character behavior, security analysis, CPU control units, natural language processing, and speech recognition .
Is DFA an NFA?
A deterministic finite automaton (DFA) can be seen as a special kind of NFA , in which for each state and symbol, the transition function has exactly one state. Thus, it is clear that every formal language that can be recognized by a DFA can be recognized by a NFA.
Which is faster NFA or DFA?
Generally speaking, DFA is faster , but NFA is more compact. The NFA is proportional to the size of the regular expression. (Informal proof: each operator node in a regular expression’s syntax just adds a new node to the NFA graph.)
Can we convert DFA to NFA?
The simple answer is Yes. Every DFA is an NFA i.e every DFA can be converted into NFA but not vice versa . But there is an equivalent DFA for every NFA.
What is the language of DFA?
That is, the language accepted by a DFA is the set of strings accepted by the DFA . Example 1 : This DFA accepts { } because it can go from the initial state to the accepting state (also the initial state) without reading any symbol of the alphabet i.e. by reading an empty string .
What does E mean in DFA?
From the definition of DFA ,”Deterministic Finite Automata is a machine that can’t move on other state without getting any input”. And since epsilon means nothing . Hence DFA can’t move on epsilon moves.
How do I create a DFA?
What is empty string in DFA?
The empty string is a sequence of symbols from the alphabet with length zero . The empty string is never a symbol in the alphabet. Your language – the language of all strings over {0, 1} with no more than four 1s – includes the empty string, since the empty string contains fewer than four 1s.
Can DFA accept empty string?
Yes. This is immediate from the definitions. A DFA accepts if it’s in an accepting state after it’s read its input . If the input is the empty string, the DFA makes no transitions so, after reading it’s input, it’s still in its initial state, q0.
Can DFA accept infinite languages?
If the language is regular, there are infinitely many DFAs that accept it . For the purposes of using the pumping lemma, it doesn’t really matter which DFA for the language you use, since any DFA will visit some state more than once if it processes an input whose length exceeds the number of states in the DFA.
Can DFA have multiple transitions?
My answer is an unequivocal: No. A deterministic finite automata does not need a transition from every state for every symbol . The meaning when δ(q,a) does not exist is simply that the DFA does not accept the input string.
How many transitions can enter a state in a DFA?
A DFA has exactly one transition from every state on every symbol in the alphabet.
How many initial states can a DFA have?
As per the definition of DFA, so as NFA it can have only one initial state . See the definition here.
How many DFA can be made if we are having 2 states and 2 inputs?
Final state can be any subset of the set of states including the empty set. With 2 states, we can have 22=4 possible sub states. Thus total number of DFAs possible : =2×24×4= 128 .
Can a DFA have all accept states?
Yes, every state can be accepting . Assuming the transition function is total (complete), so every state has a transition out on every possible letter in the alphabet, then yes, this would recognize all strings in the DFA’s alphabet: the DFA would recognize Σ∗.
How many states does a DFA have to have?
This language has the strings that have some number of 0’s followed by the same number of 1’s. Let’s start by showing that a DFA accepting L must have at least 3 states .
Is DFA a FSM?
FSM is further distinguished by Deterministic Finite Automata (DFA) and Nondeterministic Finite Automata (NFA). In DFA, for each pair of state and input symbol there is only one transition to a next state whereas, in NFA, there may be several possible next states.
How many final states can a DFA have?
DFA can only have one initial state, but can have zero, one or more than one final states over any number of input alphabet.
