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When tinkering with noncanonical LR parsing, I thought up a parsing method (with infinitely sized tables, which makes it somewhat unpractical) capable of parsing exactly the unambiguous grammars in $O(n^2)$ time, and I wondered if it is possible to do better:

Can all unambiguous grammars be parsed in linear time?

I'm quite sure I read somewhere that this is the case, but it doesn't come up when searching the internet. The same question was asked here, but no answer was given as far as I know.