hw8sol - Computer Science 340 Reasoning about Computation...

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Unformatted text preview: Computer Science 340 Reasoning about Computation Homework 8 Due at the beginning of class on Wednesday, November 21, 2007 Problem 1 The ciphertext below QFL HCVPS PX V ANSWLCEZK NCJVS; PQ XQVCQX QFL BPSZQL RNZ JLQ ZT PS QFL BNCSPSJ VSW WNLX SNQ XQNT ZSQPK RNZ JLQ QN DKVXX was created by using a substitution cipher on the alphabet of 26 letters. Recover the plaintext and show all your steps. (Hint: J decodes to G.) Solution sketch: QFL occurs a lot: say, it’s THE. Since Q goes to T and there’s the word QN, N must be O. In the word PQ, Q stands for T, so P could be I or A. The word PX could be IN, IS, AN, AS, AM, so X must be one of N,S,M. But we have XQVCQX and we know that Q stands for T: the only consonant that fits before and after a T is S, so X goes to S. The two choices of the 3rd word are IS and AS, so P goes to I and V goes to A. The last 3 letters of WNLX being OES, the only choice for W is D. Now, XQVCQX could only be STARTS, meaning C is R, so last four letters of HCVPS are RAIN. Finishing is easy: THE BRAIN IS A WONDERFUL ORGAN; IT STARTS THE MINUTE YOU GET UP IN THE MORNING AND DOES NOT STOP UNTIL YOU GET TO CLASS Problem 2 1. Find the smallest integer1....
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hw8sol - Computer Science 340 Reasoning about Computation...

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