a1 - Hint: ollow the proo that 2 is not a rational number...

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Homework 1 CS 321 Due Date: 10/6/10, 2 PM Note: The homeworks should be your own work. You can discuss the homeworks orally with your peers, however. You are allowed to use the internet sources only when you are explicitly asked to do so. In such cases, you should cite the sources and answer in your own words (don’t copy verbatim which would be considered plagiarism.) All questions carry equal weight. Please see the TA and the instructor during the ofce hours to get more help. 1. Search the web and find 3 diFerent applications o± finite state automata other than digital logic design, neural networks, and scanners. Give a brie± description or example o± each application. 2. Section 1.1. Problem 11. Show that S 1 × ( S 2 S S 3 ) = ( S 1 × S 2 ) S ( S 1 × S 3 ). Note: You need to show that every member o± the le±t hand side is a member o± the right hand side and vice versa. 3. Section 1.1. Problem 26. Show by induction on n that n X i =1 1 i 2 2 - 1 n (1) 4. Section 1.1. Problem 31. Show that 3 is not a rational number.
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Unformatted text preview: Hint: ollow the proo that 2 is not a rational number in the book. 5. Section 1.2. Problem 1. Use induction on n to show that | u n | = n | u | or all srings u and integers n 0. Hint: Use the act that u i +1 = u i u and u = . 6. Section 1.2. Problem 8. Show that ( L 1 L 2 ) R = L R 2 L R 1 . Hint: Use the ollowing act (problem 2) as given. or any strings u,v over some alphabet ( uv ) R = v R u R . Note that u R is the reverse o string u . ( L ) R is the set o reverses o strings in L . 7. Section 1.2. Problem 9. Show that ( L * ) * = L * or all languages L . 8. Section 1.2. Problem 11(b). ind a grammar or = { a,b } that generates the sets o all strings with at least one a . 9. Section 1.2. Problem 14(b). Give a grammar to generate the language L 2 = { a n b 2 n : n } . 10. Give a grammar to generate the language L * 2 , where L 2 is dened in the previous problem. 1...
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This note was uploaded on 12/04/2010 for the course CS 321 taught by Professor Staff during the Fall '08 term at Oregon State.

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