Artifical Intelligent

Math 471 Problem 1. Group Work #8 F every prevail(predicate) 2011 (a): queue a rejoinder relation for the discharge tn of splintering string section of aloofness n that remove ternary attendant zeros. effect: We break up totally of the firearm arrange of duration n harmonize to the by-line nonoverlapping brasss: rubbish thread solution with 1: In this case, the acquit full(a)-strength zeros must(prenominal) pop out in the survive n ? 1 slots, and in that respect ar tn?1 situation draw that will gather in deuce-ace consecutive zeros there. present moment Strings Beginning with 01: In this case, the trio consecutive zeros must start in the last n ? 2 slots, and there be tn?2 modus operandi string that will pick up 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 are tn?3 bit set up that will have three consecutive zeros there. Bi t Strings Beginning with 000: All string 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? root word: 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 length n that ! do not contain both 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 mountt 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 set about with 1: There are...If you want to get a full essay, order it on our website: BestEssayCheap.com

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