【编译原理】第四章作业(2)

编译原理第四章作业(2)

计科 吴政亿

• 编译原理第四章作业(2)
  
  • 151220129 计科 吴政亿
    
    • 4.6.2
    • 4.6.3
    • 4.6.6
    • 4.7.1

2

1. 增广文法:

   (0) S′→S
   (1) S→SS+
   (2) B→SS∗
   (3) B→a

2. SLR项集如下:

   • I0:S′→⋅S,S→⋅SS+,S→⋅SS∗,S→⋅a
   • I1:S′→a⋅
   • I2:S′→S⋅,S→S⋅S+,S→S⋅S∗,S→⋅SS+,S→⋅SS∗,S→⋅a
   • I3:S′→SS⋅+,S→SS⋅∗,S→S⋅S+,
            S→S⋅S∗,S→⋅SS+,S→⋅SS∗,S→⋅a
   • I4:S′→SS+⋅
   • I5:S′→SS∗⋅

3. GOTO 函数如下:
   GOTO(I0,a)=I1 , GOTO(I0,S)=I2
   GOTO(I2,a)=I1 , GOTO(I2,S)=I3 , GOTO(I2, $ )=accept
   GOTO(I3,a)=I1 , GOTO(I3,S)=I3
   GOTO(I3,+)=I4 , GOTO(I3,∗)=I5

4. 语法分析表如下：

状态	ACTION				GOTO
	a	+	*	$	S
0	S1				2
1	r3	r3	r3	r3
2	S1			accept	3
3	S1	S4	S5		3
4	r1	r1	r1	r1
5	r2	r2	r2	r2

无冲突，这显然是一个 SLR 文法

3

序号	栈	符号	输入	动作
(1)	0		aa*a+$	移入
(2)	01	a	a*a+$	按S->a规约
(3)	02	S	a*a+$	移入
(4)	021	Sa	*a+$	按S->a规约
(5)	023	SS	*a+$	移入
(6)	0235	SS*	a+$	按S->SS*规约
(7)	02	S	a+$	移入
(8)	021	Sa	+$	按S->a规约
(9)	023	SS	+$	移入
(10)	0234	SS+	$	按S->SS+规约
(11)	02	S	$	接受

6

• 因为First(SA) = First(A) = {a}，所以该文法不是LL(1)的。

• 下证该文法是SLR(1)的：

  1. 增广文法：
     (0) S′→S
     (1) S→SA
     (2) S→A
     (3) A→a

  2. SLR项集:

     • I0:S′→⋅S,S→⋅SA,S→⋅A,A→⋅a
     • I1:A→a⋅
     • I2:S→A⋅
     • I3:S′→S⋅,S→S⋅A,A→⋅a
     • I4:S→SA⋅

  3. 语法分析表:

状态	ACTION		GOTO
	a	$	S	A
0	S1		S2	S3
1	r3	r3
2	r2	r2
3	S!	acc		S4
4	r1	r1

因为没有重复的冲突项，故该文法为SLR（1）的。

1

1. 规范LR项集族

I0:
    [S' -> ·S  , $] 
    [S' -> ·SS+, $], [S' -> ·SS+, a]
    [S' -> ·SS*, $], [S' -> ·SS*, a]
    [S' -> ·a  , $], [S' -> ·a  , a]
I1:
    [S' -> a·  , $], [S' -> a·  , a]
I2:
    [S' -> S·  , $] 
    [S' -> S·S+, $], [S' -> S·S+, a]
    [S' -> S·S*, $], [S' -> S·S*, a]
    [S' -> ·SS+, a], [S' -> ·SS+, *], [S' -> ·SS+, +]
    [S' -> ·SS*, a], [S' -> ·SS*, *], [S' -> ·SS*, +]
    [S' -> ·a  , a], [S' -> ·a  , *], [S' -> ·a  , +]
I3:
    [S' -> a·  , a], [S' -> a·  , *], [S' -> a·  , +]
I4:
    [S' -> SS·+, $], [S' -> SS·+, a]
    [S' -> SS·*, $], [S' -> SS·*, a]
    [S' -> S·S+, a], [S' -> S·S+, *], [S' -> S·S+, +]
    [S' -> S·S*, a], [S' -> S·S*, *], [S' -> S·S*, +]
    [S' -> ·SS+, a], [S' -> ·SS+, *], [S' -> ·SS+, +]
    [S' -> ·SS*, a], [S' -> ·SS*, *], [S' -> ·SS*, +]
    [S' -> ·a  , a], [S' -> ·a  , *], [S' -> ·a  , +]
I5:
    [S' -> SS+·, $], [S' -> SS+·, a]
I6:
    [S' -> SS*·, $], [S' -> SS*·, a]
I7:
    [S' -> SS·+, a], [S' -> SS·+, *], [S' -> SS·+, +]
    [S' -> SS·*, a], [S' -> SS·*, *], [S' -> SS·*, +]
    [S' -> S·S+, a], [S' -> S·S+, *], [S' -> S·S+, +]
    [S' -> S·S*, a], [S' -> S·S*, *], [S' -> S·S*, +]
    [S' -> ·SS+, a], [S' -> ·SS+, *], [S' -> ·SS+, +]
    [S' -> ·SS*, a], [S' -> ·SS*, *], [S' -> ·SS*, +]
    [S' -> ·a  , a], [S' -> ·a  , *], [S' -> ·a  , +]
I8:
    [S' -> SS+·, a], [S' -> SS+·, *], [S' -> SS+·, +]
I9:
    [S' -> SS*·, a], [S' -> SS*·, *], [S' -> SS*·, +]

1. LALR项集族:

I0:
    [S' -> ·S  , $] 
    [S' -> ·SS+, $], [S' -> ·SS+, a]
    [S' -> ·SS*, $], [S' -> ·SS*, a]
    [S' -> ·a  , $], [S' -> ·a  , a]
I1:
    [S' -> S·  , $] 
    [S' -> S·S+, $], [S' -> S·S+, a]
    [S' -> S·S*, $], [S' -> S·S*, a]
    [S' -> ·SS+, a], [S' -> ·SS+, *], [S' -> ·SS+, +]
    [S' -> ·SS*, a], [S' -> ·SS*, *], [S' -> ·SS*, +]
    [S' -> ·a  , a], [S' -> ·a  , *], [S' -> ·a  , +]
I2:
    [S' -> SS·+, a], [S' -> SS·+, *], [S' -> SS·+, +], [S' -> SS·+, $]
    [S' -> SS·*, a], [S' -> SS·*, *], [S' -> SS·*, *], [S' -> SS·*, $]
    [S' -> S·S+, a], [S' -> S·S+, *], [S' -> S·S+, +]
    [S' -> S·S*, a], [S' -> S·S*, *], [S' -> S·S*, +]
    [S' -> ·SS+, a], [S' -> ·SS+, *], [S' -> ·SS+, +]
    [S' -> ·SS*, a], [S' -> ·SS*, *], [S' -> ·SS*, +]
    [S' -> ·a  , a], [S' -> ·a  , *], [S' -> ·a  , +]
I3:
    [S' -> a·  , a], [S' -> a·  , *], [S' -> a·  , +], [S' -> a·  , $]
I4:
    [S' -> SS+·, a], [S' -> SS+·, *], [S' -> SS+·, +], [S' -> SS+·, $]
I5:
    [S' -> SS*·, a], [S' -> SS*·, *], [S' -> SS*·, +], [S' -> SS*·, $]