Context Free Language Question?

Hello, I'm new to context free languages and having trouble converting from a mathematical description of a language into the CFG syntax. For example, if I'm asked to find (a^n)(b^n) for n greater or equal to zero, that is a language that has the same number as a's as b's that begins with "a", i know that I can write the context language as:


S--%26gt;aSb | e





How do I handle a situation where I have something like:


(a^m)(c^p)(d^q) such that m = p + q.





Anyone have an idea??


Thanks

Context Free Language Question?
Here's an example and a hint:





aaaaaaaacccddddd





= aaaaa ( aaaccc ) ddddd





You can easily generate the middle part with a rule. After that generate the outer part with another rule.





MORE DETAILS





One rule T must generate a number of a's followed by an equal number of 'c's : a^p c^p. The number can be 0, so includes the empty string, e.





Using T make another (main) rule S to generate a number of a's followed by T followed by an equal number of d's: a^q T d^q. The number can be 0, so includes the result of generating T.





ac is generated: T generates one of each: ac, then S generates 0 of extra a and d.





ad is generated: T generates 0 of a and c to get e, then S generates 1 of extra a and d.





Better to represent the language as





a^(p+q) c^p d^q, or as





a^q a^p c^p d^q





to see the required pattern, rather than thinking of m = p+q as a condition to be satisifed by the rules.





T --%26gt; e | a T c


S --%26gt; T | a T d