一筆交易最終的權重增長
===
先給出猜測
:::info
一筆交易a的權重增長 , 有很大的機率 , 最終會變成任何新發起的交易 , 都會增加a的權重(交易選擇算法是選tip , 盡可能不選lazy tip的算法)
:::
分兩個例子來觀察以上猜測
# 一般節點
node的網路拓樸
```graphviz
graph graphname{
1 -- 2;
2 -- 3;
3 -- 4;
}
```
node $3$ 的DAG
```graphviz
digraph init{
rankdir=RL;
a[ label="c" color=blue, fontcolor=blue, fontsize=24, shape=box];
b[label="b" color=blue, fontcolor=blue, fontsize=24, shape=box];
c[label="a" color=blue, fontcolor=blue, fontsize=24, shape=box]
e[label="e" color=blue, fontcolor=blue, fontsize=24, shape=box]
d[label="d" color=blue, fontcolor=blue, fontsize=24, shape=box]
31[label="31" color=pink, fontcolor=pink, fontsize=24, shape=box]
21[label="21" color=blue, fontcolor=blue, fontsize=24, shape=box]
41[label="41" color=blue, fontcolor=blue, fontsize=24, shape=box]
32[label="32" color=blue, fontcolor=blue, fontsize=24, shape=box]
11[label="11" color=blue, fontcolor=blue, fontsize=24, shape=box]
22[label="22" color=blue, fontcolor=blue, fontsize=24, shape=box]
42[label="42" color=blue, fontcolor=blue, fontsize=24, shape=box]
33[label="33" color=blue, fontcolor=blue, fontsize=24, shape=box]
12[label="12" color=blue, fontcolor=blue, fontsize=24, shape=box]
23[label="23" color=blue, fontcolor=blue, fontsize=24, shape=box]
43[label="43" color=blue, fontcolor=blue, fontsize=24, shape=box]
a -> c;
b -> c;
a -> c;
b -> c;
e -> a;
e -> b;
d -> a;
d -> b;
31->d;
31->d;
21->e;
21->d;
41->e;
41->d;
32->31;
32->21;
11->e;
11->e;
22->21;
22->31;
42->41;
42->31;
33->42;
33->22;
12->11;
12->21;
23->22;
23->32;
43->32;
43->42;
}
```
說明交易內 $11$ 的意義
$xy$ , $x$ 代表 node $x$ , $y$ 代表第 $y$ 秒發起的交易
所以 $11$ 代表 node $1$ 第 $1$ 秒發起的交易
看粉紅色交易 $\color{pink}{31}$ , 代表是 node $3$ 第 $1$ 秒發起的交易
注意到直接或間接指向 $\color{pink}{31}$ 的交易
直接的有 $32$ , $22$ , $42$
依照 $lazy \space tip$ 的假設
是 node $3$ 附近 latency 低的node發起的交易 , 比較容易增加 $\color{pink}{31}$ 的權重
然後看直接驗證 $32$ , $22$ , $42$ 的 $23$ , $43$ , $33$ 也會增加 $\color{pink}{31}$ 的權重
看一下 node $2$ 的DAG
```graphviz
digraph init{
rankdir=RL;
a[ label="c" color=blue, fontcolor=blue, fontsize=24, shape=box];
b[label="b" color=blue, fontcolor=blue, fontsize=24, shape=box];
c[label="a" color=blue, fontcolor=blue, fontsize=24, shape=box]
e[label="e" color=blue, fontcolor=blue, fontsize=24, shape=box]
d[label="d" color=blue, fontcolor=blue, fontsize=24, shape=box]
21[label="21" color=blue, fontcolor=blue, fontsize=24, shape=box]
11[label="11" color=blue, fontcolor=blue, fontsize=24, shape=box]
31[label="31" color=pink, fontcolor=pink, fontsize=24, shape=box]
22[label="22" color=blue, fontcolor=blue, fontsize=24, shape=box]
12[label="12" color=blue, fontcolor=blue, fontsize=24, shape=box]
32[label="32" color=blue, fontcolor=blue, fontsize=24, shape=box]
41[label="41" color=blue, fontcolor=blue, fontsize=24, shape=box]
23[label="23" color=blue, fontcolor=blue, fontsize=24, shape=box]
13[label="13" color=blue, fontcolor=blue, fontsize=24, shape=box]
42[label="42" color=blue, fontcolor=blue, fontsize=24, shape=box]
33[label="33" color=blue, fontcolor=blue, fontsize=24, shape=box]
a -> c;
b -> c;
a -> c;
b -> c;
e -> a;
e -> b;
d -> a;
d -> b;
21->e;
21->d;
11->e;
11->e;
31->d;
31->d;
22->21;
22->31;
41->e;
41->d;
12->11;
12->21;
32->21;
32->31;
23->22;
23->32;
42->41;
42->31;
13->12;
13->22;
33->22;
33->42;
}
```
$13$ 經過廣播從 node $2$ 傳到 node $3$
一秒後也會增加 $\color{pink}{31}$ 的權重
node $3$ 收到 $13$ 的DAG如下
```graphviz
digraph init{
rankdir=RL;
a[ label="c" color=blue, fontcolor=blue, fontsize=24, shape=box];
b[label="b" color=blue, fontcolor=blue, fontsize=24, shape=box];
c[label="a" color=blue, fontcolor=blue, fontsize=24, shape=box]
e[label="e" color=blue, fontcolor=blue, fontsize=24, shape=box]
d[label="d" color=blue, fontcolor=blue, fontsize=24, shape=box]
31[label="31" color=pink, fontcolor=pink, fontsize=24, shape=box]
21[label="21" color=blue, fontcolor=blue, fontsize=24, shape=box]
41[label="41" color=blue, fontcolor=blue, fontsize=24, shape=box]
32[label="32" color=blue, fontcolor=blue, fontsize=24, shape=box]
11[label="11" color=blue, fontcolor=blue, fontsize=24, shape=box]
22[label="22" color=blue, fontcolor=blue, fontsize=24, shape=box]
42[label="42" color=blue, fontcolor=blue, fontsize=24, shape=box]
33[label="33" color=blue, fontcolor=blue, fontsize=24, shape=box]
12[label="12" color=blue, fontcolor=blue, fontsize=24, shape=box]
23[label="23" color=blue, fontcolor=blue, fontsize=24, shape=box]
43[label="43" color=blue, fontcolor=blue, fontsize=24, shape=box]
13[label="13" color=blue, fontcolor=blue, fontsize=24, shape=box]
a -> c;
b -> c;
a -> c;
b -> c;
e -> a;
e -> b;
d -> a;
d -> b;
31->d;
31->d;
21->e;
21->d;
41->e;
41->d;
32->31;
32->21;
11->e;
11->e;
22->21;
22->31;
42->41;
42->31;
33->42;
33->22;
12->11;
12->21;
23->22;
23->32;
43->32;
43->42;
13->12;
13->22;
}
```
可以注意到比較久時間後 , node $1$ 發的交易也可能增加 $\color{pink}{31}$ 的權重
# 邊緣節點(edge node)
```graphviz
digraph init{
rankdir=RL;
a[ label="c" color=blue, fontcolor=blue, fontsize=24, shape=box];
b[label="b" color=blue, fontcolor=blue, fontsize=24, shape=box];
c[label="a" color=blue, fontcolor=blue, fontsize=24, shape=box]
e[label="e" color=blue, fontcolor=blue, fontsize=24, shape=box]
d[label="d" color=blue, fontcolor=blue, fontsize=24, shape=box]
41[label="41" color=blue, fontcolor=blue, fontsize=24, shape=box]
31[label="31" color=blue, fontcolor=blue, fontsize=24, shape=box]
42[label="42" color=blue, fontcolor=blue, fontsize=24, shape=box]
21[label="21" color=blue, fontcolor=blue, fontsize=24, shape=box]
32[label="32" color=blue, fontcolor=blue, fontsize=24, shape=box]
43[label="43" color=blue, fontcolor=blue, fontsize=24, shape=box]
33[label="33" color=blue, fontcolor=blue, fontsize=24, shape=box]
22[label="22" color=blue, fontcolor=blue, fontsize=24, shape=box]
11[label="11" color=blue, fontcolor=blue, fontsize=24, shape=box]
a -> c;
b -> c;
a -> c;
b -> c;
e -> a;
e -> b;
d -> a;
d -> b;
41->e;
41->d;
31->d;
31->d;
42->41;
42->31;
21->e;
21->d;
32->21;
32->31;
43->42;
43->32;
11->e;
11->e;
22->21;
22->31;
33->22;
33->42;
}
```
edge node 可以注意到
全部node發的交易會幫助 edge node發的交易增加權重 , 會是比較慢才會出現的
看 $41$ 這筆交易就可以看出
只有 $42$ , $33$ , $43$ 可以增加權重
所以edge node 發的交易 , 安全性是比較低的(權重增加的速率比較慢)
# 機率分析
# 總結
猜測:
:::info
一筆交易a的權重增長 , 有很大的機率 , 最終會變成任何新發起的交易 , 都會增加a的權重(交易選擇算法是選 $tip$ , 盡可能不選 $lazy \space tip$ 的算法)
:::
從以上模擬出來的DAG來看 , 猜測似乎是對的
而目前還提不出詳細的數學證明
###### tags: `IOTA`
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