Table of Contents
Why is ANBN not regular?
Theorem: The language L = { anbn | n ∈ ℕ } is not regular. Proof: Let S = { an | n ∈ ℕ }. This set is infinite because it contains one string for each natural number. Now, consider any strings an, am ∈ S where an ≠ am.
What are the minimum no of states required to construct a FA for the language L a 2n n >= 1?
We need minimum n+1 states to build NFA that accepts all substrings of a binary string. For example, following NFA accepts all substrings of “010″ and it has 4 states. Which one of the following languages over the alphabet {0,1} is described by the regular expression: (0+1)*0(0+1)*0(0+1)* ?Regular languages and finite automata. A A C C D D.
Can a NFA recognize the WW language?
Answer: The NFA M below recognizes the language C = { w ∈ Σ∗ | w ends with 00 }, where Σ = {0, 1}. Note that M′ accepts the string 100 ∈ C = { w | w does not end with 00 }, so M′ does not recognize the language C. Since every NFA has an equivalent DFA (Theorem 1.39), there is a DFA D such that L(D) = L(M) = C.
Why PDA is more powerful than FA?
A PDA is more powerful than FA. Any language which can be acceptable by FA can also be acceptable by PDA. PDA also accepts a class of language which even cannot be accepted by FA. Thus PDA is much more superior to FA.
Why is a * b * Regular?
Yes, a*b* represents a regular language. Language description: Any number of a followed by any numbers of b (by any number I mean zero (including null ^ ) or more times). Some example strings are: {^, a, b, aab, abbb, aabbb, }May 24, 2013.
Is the language ANBN n 0 regular?
And to do that you have to count both, the no. of ‘a’ as well as no. of ‘b’ but because value of ‘n’ can reach infinity, it’s not possible to count up to infinity using a Finite automata. So that’s why {a^n b^n | n >= 0} is not regular.
Can a null string be accepted by DFA?
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 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.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.
How many number of states required to design a NFA that accepts a language containing all binary strings where each string is starting with 0?
Explanation: We need minimum n+1 states to build NFA that accepts all substrings of a binary string. For example, following NFA accepts all substrings of “010″ and it has 4 states.
Does NFA accept empty string?
The empty string is accepted by this NFA by traversing the transition, but the initial state is non-accepting. If the claim were about DFAs, then it would be true, since lambda- (or epsilon-, or empty) transitions wouldn’t be available. Yes it is true. By defualt NFA means NFA without Epsilon transition.
What strings are accepted by NFA?
The language accepted by an NFA < Q, , q0, , A > is the set of strings that are accepted by the NFA. Some of the strings accepted by the NFA given above are , a, ab, aaa, abbbb etc. and the language it accepts is a*( ab + a + ba )(bb)* . for NFA has properties similar to that for DFA.
Can a DFA accept more than one language?
A machine may accept several strings, but it always recognizes only one language.
How can you differentiate a PDA from an FA?
Pushdown automata has the additional stack for storing long sequence of alphabets. Finite Automata doesn’t has any space to store input alphabets.
Why stack is used in PDA?
Originally Answered: Why was stack chosen as the data structure used in pushdown automata? Because, it is the only data structure that can store stuff in memory without requiring a tape or RAM. A single pair of operations can do it.
Which automata is having 7 tuples?
PDA can be betokened formally by a 7-tuple (Q, ∑, S, δ, q0, I, F) where, Q is the number of states. It is finite. ∑ is an input alphabet.
Is the empty string in every language?
Languages don’t contain sets, they contain strings, It’s true that for any language L, we have that the empty set is a subset of L, i.e. ∅⊆L, since this is true of any set. So if this is what you’re asking, then yes, that is trivially true.
Is a 2n regular?
To proof that certain language is regular, you can draw its dfa/regular expression. And you can drive do for this language as follows: Because ” anan for n >= 0 ” is same as ” a2n for n >=0″, and that is “set of all string contests of even number of symbol a ” that is regular — regular expression for this is (aa)* .
What is language in flat?
In automata theory, a formal language is a set of strings of symbols drawn from a finite alphabet. A formal language can be specified either by a set of rules (such as regular expressions or a context-free grammar) that generates the language, or by a formal machine that accepts (recognizes) the language.
Can a regular language be infinite?
Now, when a language is infinite (it has an infinite number of strings), it might be any type of a language (regular or not) in the Chomsky hierarchy.
How do you prove a language is non-regular?
Method to prove that a language L is not regular Select w such that |w| ≥ c. Select y such that |y| ≥ 1. Select x such that |xy| ≤ c. Assign the remaining string to z. Select k such that the resulting string is not in L.
Is a NB NC N context-free?
a*b*c* is a regular expression, and the intersection of its language with L is a^n b^n c^n, which is not context-free.
