Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 4F / d / Solution

TakeandThese are variable based and have disjoint variable sets. They satisfyIn $H^{\mathrm{reg}}$, however, both terminal productions of $G$ are replaced:Consequently its only terminal derivation issoThis realizes the failure of the regular concatenation construction for a nonregular grammar: two different terminal productions introduce two copies of $T$.