Nested-count context-free grammar

A context-free grammar can enforce sums such as

0^{n} 1^{m} 0^{n + m}

by nesting one matched terminal pair for each independent count.

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- Nested two-pair count language Nested-count context-free grammar

Nested two-pair count language

The language

{a^{4 r} b^{5 s} c^{2 s} d^{3 r} : r, s \geq 0}

is context-free. The grammar

S \to aaaa S ddd ∣ T, T \to bbbbb T cc ∣ ϵ

nests the

a, d

dependency around the

b, c

dependency.

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