Automata Theory Questions Medium
The pumping lemma for context-free languages is a fundamental tool used to prove that a language is not context-free. It states that for any context-free language L, there exists a pumping length p such that any string s in L with a length of p or more can be divided into five parts: uvwxy, satisfying the following conditions:
1. The length of v and y combined is greater than 0, i.e., |vxy| > 0.
2. The length of uvwxy is less than or equal to p, i.e., |uvwxy| ≤ p.
3. For any non-negative integer n, the string uv^nwx^ny is also in L.
In simpler terms, the pumping lemma states that if a language is context-free, then any sufficiently long string in that language can be "pumped" by repeating or removing a portion of it while still remaining in the language. If a language fails to satisfy the conditions of the pumping lemma, it is not context-free. This lemma provides a powerful tool for proving the non-context-freeness of certain languages.