A devise a cfg that generates any subset of these options, Basic Statistics

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A devise a cfg that generates any subset of these options

Consider n optional symbols X₁ ......X_n as described in Exercise 11.

(a) Devise a CFG that generates any subset of these options. That is, the symbols can occur in any order, any symbol can be missing, and no symbol is repeated.

(b) What is the relation between the size of your grammar and n, the number of options?

(c) How is your solution affected if symbols X_i and X_j are present only if i j?

Exercise 11

Section 4.3 describes extended BNF notation for optional and repeated symbol sequences. Suppose the n grammar symbols X_1........X_n represent a set of n options. What is the effect of the following grammar with regard to how the options can appear?

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