Virtual Labs

Pumping Lemma for CF and RL

What are the two main constraints that must be satisfied in the pumping lemma for regular languages?

a: |xy| ≤ p and |z| ≥ 1 Explanation

Explanation

b: |xy| ≤ p and |y| ≥ 1 Explanation

Explanation

c: |xyz| ≤ p and |y| ≥ 1 Explanation

Explanation

d: |y| ≤ p and |xy| ≥ 1 Explanation

Explanation

In the pumping lemma for context-free languages, how many parts is a string decomposed into?

a: Three parts: x, y, z Explanation

Explanation

b: Four parts: u, v, w, x Explanation

Explanation

c: Five parts: u, v, w, x, y Explanation

Explanation

d: Two parts: left and right Explanation

Explanation

What does pumping count i = 0 represent in pumping lemma applications?

a: The original string with no changes Explanation

Explanation

b: Doubling the pumpable segments Explanation

Explanation

c: Deleting the pumpable segments entirely Explanation

Explanation

d: Adding one extra copy of the pumpable segments Explanation

Explanation

Why is the language L = {a^n b^n | n ≥ 0} not regular according to the pumping lemma?

a: Because it contains infinitely many strings Explanation

Explanation

b: Because pumping the 'y' segment creates unequal numbers of a's and b's Explanation

Explanation

c: Because the string is too long to analyze Explanation

Explanation

d: Because it uses two different symbols Explanation

Explanation

In the context-free pumping lemma, what is the constraint on the middle portion 'vwx'?

a: |vwx| must be exactly equal to p Explanation

Explanation

b: |vwx| must be greater than p Explanation

Explanation

c: |vwx| must be less than or equal to p Explanation

Explanation

d: |vwx| can be any length Explanation

Explanation

What must be true about the segments 'v' and 'x' in context-free language pumping?

a: Both v and x must be non-empty Explanation

Explanation

b: At least one of v or x must be non-empty Explanation

Explanation

c: Both v and x must be empty Explanation

Explanation

d: v and x must have equal lengths Explanation

Explanation

How can the pumping lemma be used to prove that a language is NOT regular or context-free?

a: By showing that the language satisfies all pumping conditions Explanation

Explanation

b: By finding one string that can be successfully pumped Explanation

Explanation

c: By proving that for any proposed decomposition, pumping violates language membership Explanation

Explanation

d: By demonstrating that the language has finite size Explanation

Explanation

Why does the language {a^n b^n c^n | n ≥ 0} fail the pumping lemma for context-free languages?

a: Because it has three different symbols Explanation

Explanation

b: Because pumping cannot maintain equal counts of all three symbols simultaneously Explanation

Explanation

c: Because the strings are too long Explanation

Explanation

d: Because it's actually a regular language Explanation

Explanation

What is the fundamental reason why pumping lemmas provide necessary but not sufficient conditions for language classification?

a: Because the lemmas are incorrectly formulated Explanation

Explanation

b: Because some non-regular/non-CF languages may still satisfy pumping conditions Explanation

Explanation

c: Because pumping can only be applied to finite languages Explanation

Explanation

d: Because the lemmas work only for binary alphabets Explanation

Explanation