# Can a non-regular language satisfy the pumping lemma?

## Can a non-regular language satisfy the pumping lemma?

Note 1. Pumping lemma is a property of regular languages. In other words if a language is regular then it satisfies the above property. It may very well be true that certain non-regular languages also satisfy the above property.

### What is pumping lemma for non-regular languages?

The Pumping Lemma is used for proving that a language is not regular. Here is the Pumping Lemma.

• Let L = {0k1k : k ∈ N}. We prove that L is not regular.
• Let L = {(10)p1q : p, q ∈ N, p ≥ q}. We prove that L is not regular.
• There are 3 cases to consider: (a) v starts with 0 and ends with 0.
• #### Can pumping lemma prove a language is context free?

The pumping lemma can be used to construct a proof by contradiction that a specific language is not context-free. Conversely, the pumping lemma does not suffice to guarantee that a language is context-free; there are other necessary conditions, such as Ogden’s lemma, or the Interchange lemma.

How do you prove a language is not regular without pumping lemma?

To prove L is not regular, we assume it is regular. This gives us a specific (but unknown) pumping length p. We then show that L satisfies the rest of the contrapositive version of the pumping lemma, so it can not be regular. By the Pumping Lemma, we know there exist x, y, z such that w = xyz, |xy| ≤ p, and |y| ≥ 1.

What is a non regular language?

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

## What are non regular languages?

### Are context-free languages regular?

All regular languages are context-free languages, but not all context-free languages are regular. Most arithmetic expressions are generated by context-free grammars, and are therefore, context-free languages.

#### Which of the following does not obey pumping lemma for context free language?

Explanation: Finite languages (which are regular hence context free ) obey pumping lemma where as unrestricted languages like recursive languages do not obey pumping lemma for context free languages.

How do you prove non regularity?

How do you prove a language is context-free?

We can prove that a language is context-free if we construct a context-free grammar that generates it. Alternatively, we can create a pushdown automaton that recognizes the language. On the other hand, we use Ogden’s lemma and the pumping lemma for context-free languages to prove that a language isn’t context-free.

## Can non-regular languages be context-free?

The set of all context-free languages is identical to the set of languages that are accepted by pushdown automata (PDA). Here is an example of a language that is not regular (proof here) but is context-free: { a n b n ∣ n ≥ 0 } \{a^nb^n | n \geq 0\} {anbn∣n≥0}.

### What is pumping lemma in automata?

Pumping Lemma for Regular Languages In simple terms, this means that if a string v is ‘pumped’, i.e., if v is inserted any number of times, the resultant string still remains in L. Pumping Lemma is used as a proof for irregularity of a language. Thus, if a language is regular, it always satisfies pumping lemma.

#### What is CFG and CFL?

In formal language theory, a context-free language (CFL) is a language generated by a context-free grammar (CFG). Context-free languages have many applications in programming languages, in particular, most arithmetic expressions are generated by context-free grammars.

What is difference between regular language and context-free language?

The main difference between regular expression and context free grammar is that the regular expressions help to describe all the strings of a regular language while the context free grammar helps to define all possible strings of a context free language.

Which of the following is regular in context of pumping lemma?

## Which of the following are non regular *?

Which of the following is/are non regular? Explanation: There is no regular expression that can parse HTML documents. Other options are also non-regular as they cannot be drawn into finite automaton.

### Are all regular languages context-free?

#### What is the difference between regular language and context-free language?

Which lemma is used to show a language is non-regular?

Pumping lemma is used to show a language is non-regular /non-CFL. Bookmark this question. Show activity on this post. A language L satisfies the pumping lemma for regular languages and also the pumping lemma for context free languages.Which of the following statements about L is true?

Is the pumping lemma always true?

It is Contrapositive that means if a language does not satisfies pumping lemma, then it can not be regular language. It is always true. Then, it is also correct that p → q.

## Which is used to show a language is non-regular/non-CFL?

Pumping lemma is used to show a language is non-regular /non-CFL. Bookmark this question. Show activity on this post. A language L satisfies the pumping lemma for regular languages and also the pumping lemma for context free languages.Which of the following statements about L is true? A. L is necessarily a regular language.

### Is the pumping lemma an adversarial game?

The Pumping Lemma as an Adversarial Game Arguably the simplest way to use the pumping lemma (to prove that a given language is non-regular) is in the following game-like framework: There are two players, Y (“yes”) and N (“no”). Y tries to show that L has the pumping property, N tries to show that it doesn’t.