Compiler Design

Which one of the following statements is TRUE?

Consider the augmented grammar with {+, *, (, ), id } as the set of terminals.S' SS S + R | RR R * P | PP (S) | idIf I0 is the set of two LR(0) items {[S' S.], [S S. + R]}, then goto(closure(I0),+) contains exactly _____items.

Consider the following grammar along with translation rules. S S1 # T {Sval = S1val * Tval}S T {Sval = Tval}T T1 % R {Tval = T1val Rval}T R {Tval = Rval}R id {Rval = idval} Here # and % are operators and id is a token that represents an integer and idval represents the corresponding integer value. The set of non-terminals is {S, T, R, P} and a subscripted non-terminal indicates an instance of the non-terminal. Using this translation scheme, the computed value of Sval for root of the parse tree for the expression 20#10%5#8%2%2 is _____________.

Consider the following statements. I. Symbol table is accessed only during lexical analysis and syntax analysis. II. Compilers for programming languages that support recursion necessarily need heap storage for memory allocation in the run-time environment. III. Errors violating the condition 'any variable must be declared before its use' are detected during syntax analysis. Which of the above statements is/are TRUE?