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Mar 15, 2019 at 15:17 comment added reinierpost This is harder than I thought. I now know how to replace any right-hand side that generates only palindromes with a set of linear right-hand sides that generate the same language, but the original grammar may contain right-hand sides that do not generate only palindromes; it remains to be shown that this can be resolved by rewriting as well, but based on the lemmas needed for that, a much more direct proof is possible, so I will replace this answer with that.
Feb 11, 2019 at 8:47 comment added reinierpost Indeed, I hadn't considered that case. I will improve this answer when I have time.
Feb 10, 2019 at 13:26 comment added Yuval Filmus Counterexample: $S\to SS|00$.
Feb 10, 2019 at 0:17 comment added orlp The issue lies in "What do its right hand sides look like? Each can contain only one nonterminal that generates a language with size > 1" . That is not true with my grammar.
Feb 10, 2019 at 0:09 comment added reinierpost It's not linear.
Feb 9, 2019 at 23:30 comment added orlp I definitely think you have the right idea but I think it needs to be formalized a bit better. E.g. the grammar $S \to SS \mid aa$ forms a palindromic language but does not conform to your argument.
Feb 9, 2019 at 23:20 history answered reinierpost CC BY-SA 4.0