What does it mean for a DFA to decide a language?

The language accepted by the DFA is the set of inputs that cause it to end in an accepting state (called a final state by some authors). Therefore, the automaton accepts Σ∗ if every possible input leads to an accepting state.

Which language is accepted by NFA and DFA?

Using the subset construction algorithm, each NFA can be translated to an equivalent DFA; i.e., a DFA recognizing the same formal language. Like DFAs, NFAs only recognize regular languages. NFAs were introduced in 1959 by Michael O. Rabin and Dana Scott, who also showed their equivalence to DFAs.

Does DFA accept empty language?

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. Therefore, your DFA must accept the empty string to accept the language.

What is the language accepted by the following NFA?

What is the complement of the language accepted by the NFA shown below? Explanation: The given alphabet contains only one symbol {a} and the given NFA accepts all strings with any number of occurrences of ‘a’. In other words, the NFA accepts a+. Therefore complement of the language accepted by automata is empty string.

Can a DFA accept an empty string?

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. If q0 is an accepting state, the automaton accepts the empty string.

Is finite automata and DFA same?

DFA refers to deterministic finite automata. Deterministic refers to the uniqueness of the computation. The finite automata are called deterministic finite automata if the machine is read an input string one symbol at a time. In DFA, there is only one path for specific input from the current state to the next state.

What is the difference between DFA and NFA?

DFA refers to Deterministic Finite Automaton. A Finite Automata(FA) is said to be deterministic, if corresponding to an input symbol, there is single resultant state i.e. there is only one transition.
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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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Feb 26, 2021

Can the language of a DFA be infinite?

If an infinite language is regular, it can be defined by a dfa. The dfa has some finite number of states (say, n). Since the language is infinite, some strings of the language must have length > n. For a string of length > n accepted by the dfa, the walk through the dfa must contain a cycle.

Can DFA have infinite states?

Theorem. 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.

Does DFA have memory?

All finite automata have “state” which is a form of memory. However, some finite automata are also given auxiliary memory that they can read or write.

Can a DFA recognize multiple languages?

A machine may accept several strings, but it always recognizes only one language.

Can a DFA accept infinite string?

When there are n states and if we get strings of length greater than equal to n that means DFA must have a loop. With a loop in DFA we can accept infinite no.

Can an infinite language be regular?

Regular languages all have finite descriptions. But the set of strings in the language can be infinite. For example the language A* consists of all strings containing zero or more A symbols, and nothing else, and is certainly infinite.

What is the relation between enough accepted languages and DFA accepted languages?

6. What is the relation between NFA-accepted languages and DFA accepted languages? Explanation: The no of languages accepted by NFA and DFA is equal.

How do you know if a language is infinite?

a language is infinite if and only if contains words of unbounded length, i.e. longer than any size you may choose. that if you can show that the language contains words of unlimited size, it is indeed infinite.

How do you know if a language is finite?

Generate all of the strings of length 0 to n. Then, check every word to see if the only possible way to pump this word xyz is to make y≡λ. If every word pumps only according to this condition, then the language is finite.

How do you decide if a string W in language L is accepted by a DFA?

A string w is accepted by a DFA < Q , , q0 , , A > , if and only if *( q0 , w ) A . That is a string is accepted by a DFA if and only if the DFA starting at the initial state ends in an accepting state after reading the string.

Is palindrome an infinite language?

No. The set of all palindromes over a given finite alphabet is not a regular language; it is properly context-free.

Are all non regular languages infinite?

Any language consisting of a finite number of strings is regular. Note that this is exactly the second highlighted statement above, so, since it is logically equivalent to the first statement above, that statement must be true: Every non-regular language is infinite.

Are all regular languages co infinite?

The definition of regular language includes the empty set. It also includes the singleton language {a} , so no, not all regular languages are infinite.

Can DFA Recognise a palindrome number?

9. Can a DFA recognize a palindrome number? Explanation: Language to accept a palindrome number or string will be non-regular and thus, its DFA cannot be obtained.

Can finite automata accept palindrome string?

It doesn’t take long to realise that a finite state machine cannot recognise a palindromic sequence. That is if you want to recognise sequences like AAABAAA where the number of As on either side of the B has to be the same – then you can’t use a finite state machine to do the job.