Compiler Design: (free grammars and parsing)

Give the context-free grammar (CFG) for each of the following languages: (a) (2 pts) The set of nested addition expressions formed using the alphabet {int;+; (; ); [; ]}. The associativity of the additions must be established with brackets and adjacent brackets should be of different types. For example, [(int + int) + int]" and int + [int + (int + int)]" are strings in the language while int + int + int" and (int + (int + int))" are not in the language. (b) (2 pts) The set of all strings over the alphabet {a; b} with more a"s than b"s (c) (2 pts) The set of all strings over the alphabet {a; b; c} in the language L : {a i b j c k | j = i + k}. (d) (2 pts) The set of all strings over the alphabet {0; 1} in the language L : {0 i 1 j 0k | i ? j ? j ? k}.