推 JY:請問這是自動機與形式語言的作業嗎？ 09/24 15:54
推 KuoSheng:感謝分享！！ 09/28 11:19
as title, 因為很多人還沒有課本, 所以 po 出來跟大家分享.
0.11 Find the error in the following proof that all horses are the
same color.
CLAIM: In any set of h horses, all horses are the same color.
PROOF: By induction on h.
Basis: For h == 1. In any set containing just one horse, all
horses clearly are the same color.
Induction step: For k >= 1 assume that the claim is true for
h == k and prove that it is true for h == k + 1. Take any set
H of k + 1 horses. We show that all the horses in this set are
the same color. Remove one horse from this set to obtain the
set H[1] with just k horses. By the induction hypothesis, all
the horses in H[1] are the same color. Now replace the removed
horse and remove a different one to obtain the set H[2]. By
the same argument, all the horses in H[2] are the same color.
Therefore all the horses in H must be the same color, and the
proof is complete.
0.12 Show that every graph with 2 or more nodes contains two nodes that
have equal degrees.
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その乾いた哀愁の瞳に去來するものは何か？
失ったもの 得たもの
そして廣大なネットの狹間で彼が見たものとは？
虛像と實存と記號の中に彼は今、何を想うのか？
＜バトルプログラマーシラセ＞
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