Compiler construction 为以下语法计算自顶向下解析的FIRST和FOLLOW集

对于下面的语法，我已经计算了第一组和第二组 S->a++（T） T->T.S | S 解决方案： 消除左递归后，语法为：

S->a|+|(T)
T->aT'|+T'|(T)T'
T'->.ST'|epsilon

现在，第一组是： 第一（S）={a，+，（} 第一（T）={a，+，（} 第一（T'）={，ε}

以下几组是： 跟随＝{，$} 跟随（T）={} 跟随（T'）={}

非左递归语法和FOLLOW集合正确吗？那么有人能告诉我我是否找到了正确的解决方案吗。我不知道是否将

$

添加到

T

和

T'

的以下集合中。。。 请帮帮我

First sets, Straight forward:
S  = { a, +, ( }
T  = { a, +, ( }
T' = {epsilon, .}

Follow Sets:
S  = { ), ., $ }
T  = { ) }
T' = { ) }

As per the definition of follow from dragon book:

1. Place $ in FOLLOW(S) , where S is the start symbol, and $ is the input
right end marker .

2. If there is a production A -> aBβ, then everything in FIRST(β) except ε
is in FOLLOW(B) .

3. If there is a production A -> aB, or a production A -> aBβ, where
FIRST(β) contains ε, then everything in FOLLOW(A) is in FOLLOW(B) .

Follow of S contains ')' if we apply the rule 3:
T' -> .ST'

As per rule 3: a = . , B = S , T' = β and FIRST(T') contains 'ε', everything in Follow of T' is in Follow of S. Since follow of T' contains ')' it also becomes member of S.