Question

5. (5 points) Give context-free grammar that generate the following languages (1) (w is a binary string, and w starts and ends with the same symbol (2) the empty language (empty set)

Answer 1

1)S ->0T0 | 1T1

T -> 1T | 0T | ^ (^==empty string)

since S starts and ends with same number that is 0 or 1 , if we take any string that starts and ends with same number this grammar satisfies.

2)S -> S

This is the empty language.How many times we apply this production we get only S.

By applying this finite times we are not deriving any sentences hence the language is empty.

Note: if all the sentences can be derived by applying productions finite times that is called  language .

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