Formal Languages Questions Medium
The pumping lemma for context-free languages is a theorem that provides a necessary condition for a language to be 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 at least p can be divided into five parts: uvwxy, satisfying the following conditions:
1. For any i ≥ 0, the string uv^iwx^iy must also be in L.
2. The length of v and x combined, |vx|, must be greater than 0.
3. The length of uvwxy must be less than or equal to p.
4. The length of uv^iwx^iy must be greater than or equal to p.
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 the string while still remaining in the language. If a language does not satisfy the conditions of the pumping lemma, it cannot be context-free.