Ambiguity in parsing! Finding out if a grammar is ambiguous or not, is Undecidable! (see here). Also Undecidable to know if two grammars are the same.
Parse trees are used to give a string some Meaning in a Compiler (like that of a Programming language)
Single-tree grammars: Grammars that only have one choice with non-terminals on the RHS
(less powerful than context free languages, and equivalent to LRK grammars). Most Compilers are described with LRK grammars.
(equivalent to Context free grammars)