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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2019

Paper 1

The equations $3m=4l$ and $2n=5k$ are equivalent to
$$
m=4r,
\quad l=3r,
\qquad
n=5s,
\quad k=2s
$$
for nonnegative integers $r,s$. Hence the language is
$$
\{a^{4r}b^{5s}c^{2s}d^{3r}:r,s\geq0\},
$$
which is the <nested two-pair count language> generated by
$$
S\to aaaaSddd\mid T,
\qquad
T\to bbbbbTcc\mid\epsilon.
$$
It is therefore context-free.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 4H / b / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 4H / b / iii / Solution

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Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 4H / b / iii / Solution

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