ALGO_SP09_T2

ALGO_SP09_T2 - MAD 3512 - FLORIDA THEORY OF ALGORITHMS...

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MAD 3512 - THEORY OF ALGORITHMS FLORIDA INT'L UNIV. TEST #2 - Sprinq 2009 Answer all 6 questions. Provide all reasonin An unjustified answer will receive little or question on a separate page. TIME: 75 min. and show all working. 0 credi t. Begin each (15) 1. (15) 2. (18) 3 (a) (16) 4(a) (16) 5 (a) (20) 6. Find an NFA which is equivalent to th ~ RLG given below. G: S-A, S-10B, A-01A, A-1C B-OD, B-010, C-A, C-D, D-10, D-01. Convert the NFA shown below on the ight in Qu. #3 into an equivalent RLG. If B, AuB, and ACuBcare all regular languages that A must be regular? (Justify your answe l If C and D are both non-regular languages, does it that C.D must be non-regular? (Justify your nswer) [You may use any result that was proved in cl ss for Let L be the language accepted by the NFA shown on the right. Find NFAs which accept (a) U (b) (U)R. 0 b always follow always follow Probl em #4 ] ~ (a) (b) (b) Find a regular expression for the language accepted by the NFA shown on the right. Write down what the Halting Problem says and define what is a primitive Recursive function. 1/ C5j R Determine which of the following languages ar not. regular and which are (b ) L2 = { ~k . C n: k > n 2 - 1 } [If you say that it is regular, you must fin~ a regular expression for it; if you say it is non-regular, you must g~ve a complete proof.] ". (b)
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ALGO_SP09_T2 - MAD 3512 - FLORIDA THEORY OF ALGORITHMS...

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