LL1布尔运算符Grammar实现Recursive的解析器

Question

Here is the small chunk from original Grammar for which i have to implement the recursive decent parser. We have to remove the ambiguity, left recursion etc from it so that we can implement its parser. I have done the other bits, but can't figure out how to handle the not operator (~).

The valid expression could be. 1 & ~1, (1 & ~1) etc

I have handle the braces, as well as & and or symbol but can't handle the ~ symbol.

Here is the orginal grammar.

A -> A & A 
A -> ~A
A -> (A)
A -> 0 | 1

I can't figure out how to handle the ~ .

Here is my solution:

one -> two one'
one' -> ~one|^
two -> three two'
two' -> & three two'|^
three -> four three'
three' -> || four three' | ^
four -> (one) |0 |1 

When i implemented it , everything works fine for brackets, and , or operator . But the negation ~ was not working. So i believe the grammer is not properly converted to LL(1)

Answer 1

Finally, i have solved it myself after spending quite a lot of time. Here is the solution.

The boolean not or (~) operator has the highest precedence then any other operator in the grammar mentioned above. In the above solution, i was taking its precedence as lower. Here is the proper solution.