Question 6 ( 44=16 points) These questions are slightly tougher and may require to think deeply. Please attend office hours- we are here to help! 1. Consider the language consisting of strings that represent the list of numbers separated by commas. For instance, the string "10, 7 " and " 1,7,5,13 " are in the language; also included in the language are lists of a single number (e.g., "12"). Write an unambiguous BNF grammar for the language. Briey explain why your grammar is unambiguous. 2. S>aSaSbb Is this grammar ambiguous? Why? Can we remove its ambiguity if it is ambiguous (provide a replacement grammar)? 3. The following grammar for arithmetic expressions allows addition, subtraction, as well as a unary operator " " for negation; that is, " 8 " is interpreted as the number negative eight. ede+eeee 0123456789 The grammar is clearly ambiguous. Change the grammar so that "+"and "-" are left-associative and the precedence of " " is higher than " + " and "-". 4. Do context-free grammars represent all regular languages? And do regular languages translate all grammars? Are there any languages CFGs may not be able to represent? (Explain each answer in 10 words) (23=6pt)