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109年 - 109 教育部公費留學考試：離散數學#125735
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題組內容
1. Prove the following two statements.
(a)
其他申論題
(三)請舉出兩種繞過網路審查的技術,並比較其效能和適用情況。
#534237
(一)請說明何謂旁通道攻擊(side-channel attacks)。
#534238
(二)請說明上方Meltdown 範例程式的運作原理。
#534239
(三)請提出兩種防範或緩解 Meltdown 漏洞的方法,並討論其可行性。
#534240
(b) Use the formula from (a) to prove
#534242
(a) What is the coefficient of in the expansion of ?
#534243
(b) Use the result of (a) to compute the coefficient of in the expansion of .
#534244
3. Prove or disprove the following statement. Given a bipartite graph, if the number of vertices of odd degree on the left subgraph (subgraph A below) is odd, then the number of vertices of odd degree on the right subgraph (subgraph B below) is also odd.
#534245
4. Simplify the Boolean formula tr(M²) given the matrix M below with as few operations (AND, OR) as possible. The trace of a square matrix, denoted as tr(*) is defined by the summation of all diagonal elements in the matrix.
#534246
5. Convert the following finite state machine to another machine where every two transitions becomes one. That is, we have two alphabets, one after another in each transition in the new machine while all the states remain to be the same to the original machine. We assume the starting state is A.
#534247
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