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ALGO_SP08_T1 - MAD 3512 TEST THEORY OF ALGORITHMS#1...

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(15) (15) (20) (15) (20) (15 ) MAD 3512 - THEORY OF ALGORITHMS FLORIDA INT'L UNIV. TEST #1 - SPRING '08 TIME: 75 min. Answer all 6 questions. Provide all reasioning and show all working. An unjustified answer will receive ,little or no credit. BEGIN EACH QUESTION ON A SEPARATE PAGE. 1. (a) Define what is the extended transi - tion function of a DFA. (b) Convert the NFA on the right into an equivalent DFA. Find regular expressions which describe the languages below (a) Ll = {~E{a,b}*: ~ contains both aab ~ bab as substrings} (b) L2 = {~E{O,l}*: ~ has at most one ocqurrence of 01} 2. 3. 4. 5. 6. (a) (b) Find all the inaccessible states im the DFA below. Then partition the remaining sQates into blocks of indistinguishable states and find the reduced machine. w CW C -?>D @ G) G H I ~--------------- 01 D G B B (jI CAB 11 F BFA E, A H G (a) Find a DFA which accepts precisely the strings in the language L4 = {CD E{a,b}*: [nb(CD) -n)(CD) -1] (mod 4) < 2}. Verify your DFA works with babb a,s input. (b) (a) Define what are unreachable pioductions and non- terminating productions in a CFG G.1 Find
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