hw3_solution

# hw3_solution - CS150 Homework 3 Due 5/15 Problem 1....

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CS150 Homework 3 Due 5/15 Problem 1. (Exercise 4.1.1 (d) (f), 10 points) Prove that the following are not regular languages. (d) { 0 n 1 m 2 n | n and m are arbitrary integers } . (f) { 0 n 1 2 n | n 1 } (d) Proof. Assume the language L is regular, let p be the pumping-lemma constant. Pick w = 0 p 12 p . Then when we write w = xyz , we know that | xy | ≤ p , and therefore y consists of only 0’s. Thus, xz , which must be in L if L is regular, consists of fewer than p 0’s, followed by a 1 and exactly p 2’s. That string is not in L , so we contradict the assumption that L is regular. / (f) Proof. Assume the language L is regular, let p be the pumping-lemma constant. Pick w = 0 p 1 2 p . Then when we write w = xyz , we know that | xy | ≤ p , and therefore y consists of only 0’s. Thus, xz , which must be in L if L is regular, consists of fewer than p 0’s, followed by exactly 2 p 1’s. That string is not in L , so we contradict the assumption that L is regular. / 1

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Problem 2. (Exercise 4.1.2 (c), 10 points) Prove that the following are not regular languages. (e) The set of strings of 0’s and 1’s that are of the form
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## This note was uploaded on 03/31/2008 for the course CS 150 taught by Professor Jiang during the Spring '07 term at UC Riverside.

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hw3_solution - CS150 Homework 3 Due 5/15 Problem 1....

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