Given the following grammar:
Check whether it is CLR(1) or not.
I have drawn the canonical itemsets as well as the parse table. But I'm not sure whether it is actually correct or not. I have tried searching for some similar examples that have epsilon productions but could not find any. Could someone please help me out?
The initial state of your parser is I0
, and $
is the only lookahead-terminal for which I0
has an action. So if the input is anything other than the empty string, your parser will raise an error. But the grammar has non-empty strings in its language. So this can't be a correct parser for the grammar.
I think your main mistake is in propagating lookaheads. For example, when you close A -> .AB, $
, you need to add A -> .whatever
items with lookaheads equal to each terminal in FIRST(B$)
, and you haven't done that.