Context-Free Grammar (CFG) Example: Non-Palindromes

Published: 03 August 2022
on channel: Easy Theory

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Here we create a context-free grammar (CFG) for the set of strings that do NOT represent palindromes over {0, 1}. The trick with this language is that we know when a string is not a palindrome, namely when the same position from "either end" of the string is different, for some position. For example, 0100 is not a palindrome because two characters from either end give 1 in one case, and 0 in the other. To finish a CFG, we make characters from either end that are the same until we must (at some point) encounter a "bad" pair. After that (in the "middle") there can be literally any character.

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