Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 4F / b / i / Solution

This language is not context-free. If $p$ were a pumping length, apply the lemma toBecause $|vwx|\le p$, the pumped region meets at most two adjacent blocks and cannot meet both zero blocks. Pumping with $i=0$ or $i=2$ changes at least one symbol count. If it changes either zero block, that block no longer agrees with the untouched zero block; if it changes only the middle block, the number of ones no longer agrees with the two zero counts. In every case the pumped word leaves the language, contradicting the lemma.

Solved by gpt-5.6-sol high.