for ambiguous grammars, will lmd + rmd >= #pt be more accurate? since the question says "for a given string", it may be possible that the given string has lmd = rmd and only one parse tree but the CFG itself is ambiguous.
@atulcse Grammar is ambiguous if it has more than one RMD or more than one LMD and each LMD or RMD corresponds to a parse tree.
If a grammar has 1 LMD and 1 RMD its parse tree will be same and the language is not ambiguous.
I have a doubt here @raja11sep @ankit3009
For a given string and some ambiguous grammar producing it, is #LMD = #RMD always true?
For a grammar, it’s true that if every string has only 1 parse tree then it’s unambiguous. But, I’m asking for an aribitrary string in that grammar. It may still happen that some string has only 1 parse tree in an ambiguous grammar, right?
@atulcse For an unambiguous grammar every string produced by it will have 1 parse tree. But for a given string many grammars may produce it and some of them can be ambiguous too. If that grammar is ambiguous so there will exist more than 1 parse tree for that given string according to that ambiguous grammar production rules.
A grammar is ambiguous if either 2 or more parse trees/ 2 or more LMD / 2 or more RMD can be made for that grammar. So @adad20 you are right.
I don’t know about any such relations :(
May refer this, though not sure : https://gateoverflow.in/168440/Derivations