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Is it possible to build a parsing algorithm that build a parse tree using a top-down method that simulate a derivation process for regular expressions, like we do for type 2 languages?

My guess

Given a regular expression r, build its FSA, then obtain the grammar that generate r in order to build a parse tree

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    $\begingroup$ It's not clear to me what your question is. A regular expression is not a grammar (and there is no obvious unique homomorphism between regular expressions and regular grammars), so I'm not sure what you expect to be the parse tree. I suppose you could try recursively mapping substrings to subpatterns in the regular expression, but in many cases there are multiple possible mappings. $\endgroup$ – rici Nov 3 '17 at 18:46
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It is absolutely possible and you are on the right track. You will need to make sure your grammar is %100 correct and probably LL(1), from there you can choose one of many algorithm examples that are out there or write your own.

See https://en.wikipedia.org/wiki/Top-down_parsing and https://en.wikipedia.org/wiki/LL_parser

Word of warning: The tricky part won't be the implementation but getting your grammar right.

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