论文标题
关于傅立叶 - 莫兹金消除的注释，三个消除变量
A Note on Fourier-Motzkin Elimination with Three Eliminating Variables
论文作者
论文摘要
在本说明中，我们显示了蛮力傅立叶摩托犬消除的困难，即使在一个简单的情况下，有三个消除变量。具体而言，我们首先给出了一个定理，该定理在多个访问窃听（MAC-WT）频道的信息理论安全性中起着非常重要的作用，然后通过直接使用傅立叶 - 莫茨金程序直接与三个用户证明了这一点。结果表明，在消除程序中产生了大量的不平等，而大多数是多余的。实际上，生成的不等式的数量随用户数量或消除变量的数量增长了双重增长。因此，直接以这种蛮力的方式直接证明定理变得难以控制。除了极大的复杂性外，直接策略的另一个缺点是它仅在给出用户数量的情况下起作用。显然，这使得该策略不适合证明该定理，因为这是任何数量用户的一般结果。因此，通常证明定理是紧迫和挑战。
In this note, we show how difficult the brute-force Fourier-Motzkin elimination is, even in a simple case with three eliminating variables. Specifically, we first give a theorem, which plays quite an important role in the study of information-theoretic security for a multiple access wiretap (MAC-WT) channel, and then prove it for the case with three users by directly using the Fourier-Motzkin procedure. It is shown that large amounts of inequalities are generated in the elimination procedure while most of them are redundant. Actually, the number of generated inequalities grows doubly exponentially with the number of users or eliminating variables. It thus becomes unmanageable to directly prove the theorem in this brute-force way. Besides the great complexity, another disadvantage of the direct strategy is that it works only if the number of users is given. Obviously, this makes the strategy inappropriate for the proof of the theorem since it is a general result for any number of users. It is thus urgent and challenging to generally prove the theorem.
