Assignment 1: Context Free Grammars

Assignment 1: Context Free Grammars
Due: 9/30/03

Let G be defined by:

< S > < A > < B >

< A > < A > a

< A > b < B >

< B > a

< B > < S > b
1. Give a leftmost and a rightmost derivation of the string baabaab in the grammar G.
2. Show a derivation tree for baabaab relative to G.
(part of problem 4.2 from Aho, Sethi and Ullman) What language is generated by the grammar:

< S > a < S > b < S >

< S > b < S > a < S >

< S >

Justify your answer!
Show that the grammar

< S >
( < A > )

< S > b

< A > < S >

< A > < A > , < A >

is ambiguous and construct an unambiguous grammar for the same language. Include an informal description of the language generated by the grammar.
(Problem 4.4 from Fischer and LeBlanc) A production of the form A A is said to be left-recursive Similarly, a production of the form B B is said to be right-recursive. Show that any grammar that contains both left and right recursive productions with the same left-hand side symbol must be ambiguous.