Detect a class of a grammar having its DSL AST

Let I have a grammar for some language written in some DSL for writing grammars, and this DSL implements EBNF. I have an AST for the description of a grammar in the DSL. How can I detect the minimal class of the grammar (LL(1), LL(*), LR(1), PEG, etc) without constructing tables, just analysing the AST?