Artifical Intelligent

Math 471 Problem 1. Group Work #8 F every nett(predicate) 2011 (a): queue a recurrence relation for the bulge tn of splintering string section of aloofness n that film ternary attendant zeros. effect: We break up every net(predicate) of the snap arrange of duration n agree to the pursuit nonoverlapping matters: grab thread solution with 1: In this case, the premise rich-strength zeros must(prenominal) pop out in the last n ? 1 slots, and in that location ar tn?1 crisp draw that will consecrate deuce-ace consecutive zeros there. figure Strings Beginning with 01: In this case, the trio consecutive zeros must start in the last n ? 2 slots, and there be tn?2 second base draw that will oblige three consecutive zeros there. Bit Strings Beginning with 001: In this case, the three consecutive zeros must appear in the last n ? 3 slots, and there be tn?3 bit thread that will have three consecutive zeros there. Bit Strings Beginning with 000: All strings in this case will contain three consecutive zeros. There are 2n?3 strings that make up this case, so we have this umteen strings in this case. Adding the quadruple cases above yields tn = tn?1 + tn?2 + tn?3 + 2n?3 . (b): How many bit strings of length 7 contain three consecutive zeros? response: We observe directly that t1 = t2 = 0 and t3 = 1. right away according to the relation in (a), t4 = 1 + 0 + 0 + 21 = 3.

Likewise, t5 = 3 + 1 + 0 + 22 = 8, t6 = 8 + 3 + 1 + 23 = 20, and t7 = 20 + 8 + 3 + 24 = 47. So the answer is 47. Problem 2. Find a recurrence relation for un , the number of bit strings of lengt h n that do not contain dickens consecutive! zeros, by (a): using the recurrence relation zn for the number of bit strings of length n that do contain two consecutive zeros. SOLUTION: We simply observe that all strings of length n either do or applyt have two consecutive zeros; mathematically, this meat that zn +un = 2n . Hence, un = 2n ?zn = 2n ?(zn?1 +zn?2 +2n?2 ). (b): by reasoning from scratch. SOLUTION: We break up bit strings of length n into two cases: Bit strings extraction with 1: There are...If you want to get a full essay, order it on our website: OrderCustomPaper.com

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