# sample1 - Faculty of Arts and Science School of Computing...

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Faculty of Arts and Science School of Computing CISC223 Sample First Midterm Examination Instructor: D.B. Skillicorn Fall Term 2010 Instructions : 1. You have ﬁfty minutes. Attempt all questions. 2. You may bring in one 8.5x11 sheet of paper containing notes, and use it during this midterm. 3. Answer questions on the examination paper. Nothing else will be marked. Use the amount of space under each question as a guide to the detail of your answer. You may use scrap paper and the back of the examination paper pages for rough working. 4. If you do not understand a question, make reasonable assumptions, write them down and proceed. No questions will be answered during the examination. 5. Make sure your name is on every page of the examination paper. 6. Each question is labelled with an estimate of how long it should take. The actual midterm counts for 5% of your ﬁnal grade. NAME: STUDENT NUMBER

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Student number: Page 2 of 6 1. (10 minutes) Consider the following languages over the alphabet { a,b } . L 1 = { aba,aab } L 2 = { λ,aab,baa } L 3 = { λ } What are the following languages: L 1 L 2 L 1 L 2 L 2 L 3 L 1 L 3 L 1 .L 2 L 3 L * 3 2. (20 minutes) Let FINITE be the class of ﬁnite languages over some alphabet. Explain what is meant by FINITE REG . Provide three diﬀerent proofs of this statement, using regular grammars, ﬁnite state automata, and regular expressions. 3. (12 minutes) Give a regular expression that describes the language { a 2 n | n 0 } , and a regular grammar that generates it. 4. (5 minutes) Give a regular expression for the language of strings over the alphabet { a,b } that do not end in ab . 5.
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## This note was uploaded on 01/25/2011 for the course CISC 223 taught by Professor Mr.elienasr during the Spring '10 term at American University of Science & Tech.

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sample1 - Faculty of Arts and Science School of Computing...

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