Reading: Chapter 2 Context-Free Languages, Chapter 3 Church-Turing Thesis

The assignment:

• (6 points) Problem 2.18 page 130, for Part b. you may assume that the language B = {aⁿbⁿcⁿ | n ≥ 0 } is not context-free.
• (5 points) Problem 2.30 part d. page 131 (Hint: let s = a^pb^p#a^pb^p and proceed as in the text's solution for Part c.).
• (5 points) Problem 2.35 page 131 (hint: assume G generates string w of length n using a derivation of at least 2^b+1 steps. By problem 2.26, n ≥ (2^b+1 + 1)/2 > 2^b. Consider a minimal node parse tree of w, and proceed as in the proof of the Pumping Lemma).
• (6 points) Problem 3.1 parts a., b., and c. only; page 159
• (8 points) Problem 3.8 parts a., and b. only; page 160