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ALGO_SP08_T2

# ALGO_SP08_T2 - MAD 3512 TEST#2 THEORY OF ALGORITHMS FLORIDA...

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MAD 3512 - THEORY OF ALGORITHMS FLORIDA INT'L UNIV. (15) 1. TEST #2 - Sprinq 2008 Answer all 6 questions. Provide all reasoning working. An unjustified answer will receive little Begin each question on a separate page. 01 ~0' TIME: 75 min. and show all or no credi t . Let L be the language accepted by the NFA shown on the right. Find NFAs which accept (a) LC (b) (LC) R . 011 (18) 3 (a) Find a regular expression for the language accepted by the NFA shown on the right. (b) Write down what the Halting Problem says and define what is the Busy-beaver function. ? (18) 4(a) Define what are the initial functions and what is the operation known as primitive recursion. (b) Show that f (x,y) = 3x+4y+1 is a primi tive recursive function by finding primitive recursive functions g and h such that f = prim.rec. (g,h) . [You must show that your g and h are primitive recursive. ] (16) 5 (a) Define what is a Turing comput- able function with domain D. (b) Show what happens at each step if 01010 is the input for the TM, M shown on the right. (c) Find the language accepted by M. 0/11<

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ALGO_SP08_T2 - MAD 3512 TEST#2 THEORY OF ALGORITHMS FLORIDA...

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