Why are palindromes not regular languages?

Why are palindromes not regular languages?

x = 0i, y = 0j and z = 0k110n, where i + j + k = n. Now, consider xz. By the pumping lemma, xz must be in the language. This means that the set of palindromes doesn’t satisfy the pumping lemma and, thus, the set of palindromes cannot be regular.

Which of the following languages is regular?

Which of the following languages is regular? Explanation: (C) Strings which are the part of this language are either 0w0 or 1w1 where w is any string in {0, 1}* . Thus, language given in option (C) is regular.

Are palindromes context free?

Although the set of palindromes is not a regular language, it is a context free language.

Does DFA accept palindrome?

Language to accept a palindrome number or string will be non-regular and thus, its DFA cannot be obtained.

How do you prove that a language is not regular?

Method to prove that a language L is not regular

1. Select w such that |w| ≥ c.
2. Select y such that |y| ≥ 1.
3. Select x such that |xy| ≤ c.
4. Assign the remaining string to z.
5. Select k such that the resulting string is not in L.

What makes a language non regular?

Definition: A language that cannot be defined by a regular expression is a nonregular language or an irregular language.

Can palindrome be odd?

Explanation: String formed by characters at odd indices: bzb, which is a Palindrome. String formed by characters at even indices: aza, which is a Palindrome. Hence, the given string is an Even-Odd Palindrome.

How to prove a palindrome is not a regular language?

Since DFA doesn’t have memory so it wont be possible to make a DFA for this, but xR = 0^n1^n and L=x.xR that is 1^n0^n.0^n1^n is still palindrome but not a regular language. So we can say palindromes are not regular. I remember from my undergrad class to prove some language is not regular it is sufficient to give one negative example.

Is it possible to do recursion on a palindromic expression?

It’s not possible. Palindromes aren’t defined by a regular language. (See, I DID learn something in computational theory) Though, as many have pointed out, this can’t be considered a regular expression if you want to be strict. Regular expressions does not support recursion.

Are palindromes regular in DFA?

Since DFA doesn’t have memory so it wont be possible to make a DFA for this, but xR = 0^n1^n and L=x.xR that is 1^n0^n.0^n1^n is still palindrome but not a regular language. So we can say palindromes are not regular.

What are some examples of palindromic music?

British composer Robert Simpson also composed music in the palindrome or based on palindromic themes; the slow movement of his Symphony No. 2 is a palindrome, as is the slow movement of his String Quartet No. 1.