Consider the following grammar:

$$\eqalign{ & S \to S \cr & S \to SS\,|\,a\,|\,\varepsilon \cr} $$

(a) Construct the collection of sets of LR(0) items for this grammar and draw its go to graph.

(b) Indicate the shift-reduce and reduce-reduce conflict (if any) in the various state of the LR(0) parser.

The complement(s) of the element 'a' in the lattice shown in Fig. is (are) ........... .

Solve the recurrence equations:
$$\,\,\,\,\,\,\,\,\,\,T\left( n \right) = \left( {{n \over 2}} \right) + 1$$
$$\,\,\,\,\,\,\,\,\,\,\,T\left( 1 \right) = 1$$

State an undesirable characteristic of each of the following criteria for measuring performance of an operating system:
(a) Turn around time. (b) Waiting time.