CS 4511 Spring Semester, 2013

30 Points

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Reading: Chapter 2 Context-Free Languages, Chapter 3 Church-Turing Thesis
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The assignment:
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- (6 points) Problem 2.18 page 156 (page 130 of 2nd Ed.),
for Part b. you may assume
that the language B = {a
^{n}b^{n}c^{n}| n ≥ 0 } is not context-free. - (5 points) Problem 2.30 part d. page 157 (page 131 of 2nd Ed.) (Hint:
let s = a
^{p}b^{p}#a^{p}b^{p}and proceed as in the text's solution for Part c.). - (5 points) Problem 2.35 page 157 (page 131 of 2nd Ed.)
(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 187 (page 159 of 2nd Ed.)
- (8 points) Problem 3.8 parts a., and b. only; page 188 (page 160 of 2nd Ed.)