# 2001a2 - u | = | v | = | z | xyuvz ∈ L Prove that L may...

This preview shows page 1. Sign up to view the full content.

COSC 2001: Introduction to the theory of computation Assignment 2 (Released February 28, 2006) Submission deadline: 4 pm, Mar 15, 2006 1. The assignment can be handwritten or typed. It MUST be legible. 2. You may do this assignment individually or in groups of two. If you work in a group, hand in only one copy of the solutions. 3. Submit this assignment only if you have read and understood the policy on academic honesty on the course web page. If you have questions or concerns, please contact the instructor. 4. Use the dropbox near the main oﬃce to submit your assignments. No late submissions will be accepted. Question 1 [5 points] Consider any regular language L . Let L 0 be the language obtained by removing the middle ﬁfth of the strings in L . Thus L 0 = { xyvz |∃ u, | x | = | y | = |
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: u | = | v | = | z | , xyuvz ∈ L } . Prove that L may not be regular. Question 2 [4 points] Consider the CFG with rules S → aSbScS | aScSbS | bSaScS | bScSaS | cSaSbS | cSbSaS | ± Does this generate the language { x ∈ { a, b, c } * | n a ( x ) = n b ( x ) = n c ( x ) } where n a ( x ) (respectively n b ( x ) , n c ( x )) is the number of a’s (respectively, b’s, c’s) in string x ? Question 3 [3 points] Describe the language generated by a CFG with rules S → aS | aSbS | ±. Characterize the language by describing a property that every preﬁx of a string in this language must have. Question 4 [3 points] Show using the pumping lemma that the following language is not a CFL: L = { a n b m a n b n + m } . 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online