Context-Free Grammar (CFG) Example: Nested Pairs

Published: 03 August 2022
on channel: Easy Theory

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Here we create a context-free grammar (CFG) for the set of all strings of the form 0^n 1^m 2^m 3^n, where n, m are at least 0. This is often called "nested pairs" because the n's are on the outside, and the m's are on the inside. We can effectively just make a CFG for the canonical context-free language 0^n 1^n, and modify it to first handle the 0's and 3's, and then once those are done, transfer control to another variable to handle the 1's and 2's, since m and n are unrelated to each other.

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