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Unformatted text preview: CSE 260 Sample Final Exam– ANSWERS Name: This sample test gives a general idea about the type of questions that may appear in the final exam and does not necessarily include every possible type of questions that may be asked in the final exam. You should practice this sample test as well as go through all the materials that were covered in the class. 1. (a) The mod function is defined as: mod p : Z → Z ( p ), mod(x,p)=x mod p, and Z ( p ) = { , 1 , 2 , ...p 1 } We can define add and multiplication in modulo arithmetic based on the following: a + p b = ( a + b ) mod p and a * p b = ( a.b ) mod p, where a, b²Z ( p ) The addition and the multiplication table for the + 2 , * 2 , re spectively, are as follows: + 2  0 1 * 2  0 1  0 1  0 1  1 1  0 1 i. (5 points) Give the tables for + 3 and * 3 + 3  0 1 2 * 3  0 1 2  0 1 2  0 1  1 2 1  0 1 2 2  2 1 2  0 2 1 ii. (10 points) Give the following sum and product in base 3: 121 3 211 3 +220 3 * 211 3 ——— ——— 1111 3 122221 3 (b) (5 points) Which integers between 20 and 30 are relatively prime to 30. (23, 29) 2. (15 points) Consider the following grammar G = ( V, T, S, P ), where V = { S, A, a, b, c } , T = { a, b, c } and the set of produc tion rules P = { S → aSb, S → A, A → cA, A → λ, } (a) Give a derivation for the word aacccbb S ⇒ aSb ⇒ aaSbb ⇒ aaAbb ⇒ aacAbb ⇒ aaccAbb ⇒ aacccAbb ⇒ aacccbb (b) Give the parse tree for the word. S a S b a S b A c A c A c A lambda (c) Give the language generated by the above grammar. { a i c * b i  i ≥ } 3. (12 points) Answer the following true/false (a) 000110 ² * 1 * * true (b) λ² * 1 * * true (c) Following is a set of valid production rules for a regular gram mar: false S → aS S → Sb S → c (d) (1(((1 ∪ 0)1)1)) is a valid regular expression. true (e) 1001 ² (1(((0 * ∪ 1)0)1)) true (f) Regular expression (1(((1 ∪ 0) * 1)1)) is equivalent to the regular expression...
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 Spring '08
 SaktiPramanik
 Regular expression, Regular language, Nondeterministic finite state machine, Row row row, Modulo operation

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