Solution

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

For grammars $G=(\Sigma,V,P,S)$ and $G'=(\Sigma,V',P',S')$ with disjoint variable sets, introduce a new variable $S_0$ and set
$$
H=(\Sigma,V\cup V'\cup\{S_0\},
P\cup P'\cup\{S_0\to SS'\},S_0).
$$
If both input grammars are variable based, then $L(H)=L(G)L(G')$.


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