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4.4.1 第6题答案有误 #217

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4.4.1 第6题答案有误 #217

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29 changes: 15 additions & 14 deletions ch04/4.4/4.4.md
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Original file line number Diff line number Diff line change
Expand Up @@ -51,7 +51,7 @@
</table>

2. S -> + S S | \* S S | a

step1. 无左公因子

step2. 无左递归
Expand Down Expand Up @@ -90,7 +90,7 @@

S -> A
A -> (S) S A | ε

step3. 预测分析表

<table>
Expand Down Expand Up @@ -127,13 +127,13 @@

S -> SA | (S) | a
A -> +S | S | *

进一步提取终结符

S -> SA | T
A -> +S | S | *
T -> (S) | a

step2. 消除左递归(根据 p135 的算法 4.19)

i = 1
Expand All @@ -149,7 +149,7 @@
无需处理
j = 2
无需处理

得到最终的产生式

S -> TB
Expand All @@ -163,7 +163,7 @@
first(A) = [+, *] + first(T) =[+, *, (, a]
first(B) = [ε] + first(A) = [ε, +, *, (, a]
first(S) = first(T) = [(, a]

follow(T) = [$, +, *, (, a]
follow(A) = [$, +, *, (, ), a]
follow(B) = [$]
Expand Down Expand Up @@ -268,7 +268,7 @@
follow(bexpr) = follow(bexpr') = [), $]
follow(bterm) = follow(bterm') = [or, $]
follow(bfactor) = [and, $]

````

step4. 预测分析表
Expand Down Expand Up @@ -326,8 +326,8 @@
</tr>
<tr>
<th>bterm'</th>
<td></td>
<td>bterm' -> and bfactor bterm'</td>
<td>bterm' -> ε</td>
<td></td>
<td></td>
<td>bterm' -> ε</td>
Expand All @@ -349,21 +349,22 @@
</tbody>
</table>


### 4.4.2 ！！

有没有可能通过某种方法修改练习 4.2.1 中的文法，构造出一个与该练习中的语言（运算分量为 a 的后缀表达式）对应的预测分析器？

#### 解答

S -> SS+ | SS* | a

step1. 提取左公因子

S -> SSA | a
A -> + | *

step2. 消除左递归

i = 1
S -> aB
B -> SAB | ε
Expand All @@ -373,7 +374,7 @@ step2. 消除左递归
S -> aB
B -> aBAB | ε
A -> + | *

step3. 预测分析表

<table>
Expand Down Expand Up @@ -413,7 +414,7 @@ step3. 预测分析表
</tr>
</tbody>
</table>

​

### 4.4.3

Expand Down Expand Up @@ -472,7 +473,7 @@ step3. 预测分析表
以下题目请参考 Aho 本人的讲义：[Aho: Properties of Context-Free Languages](http://www.cs.columbia.edu/~aho/cs3261/lectures/12-10-08.htm)，[本地副本](cs.columbia.edu-aho-cs3261-properties-of-cfl-121008.html)

此外还有[另一篇内容相似的文章](http://courses.engr.illinois.edu/cs373/Lectures/lec14.pdf)，[本地副本](courses.engr.illinois.edu-cs373-lec14.pdf)

关于 CNF 和 CYK 算法，有较多相关资料，自行搜索

### 4.4.6 !
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