针对SysY语言中简单算术表达式文法G[E]: E→TE’ ; E’→ATE’|ε ; T→FT’ ; T’→MFT’ |ε ; F→(E) | i ; A → + | - ; M → * | / 求解相应的FIRST、FOLLOW集，构造预测分析表，并编写LL(1)语法分析程序

首先，我们来求解该文法的FIRST集和FOLLOW集。

FIRST集：

- FIRST(E) = {i, (}
- FIRST(E') = {+, -, ε}
- FIRST(T) = {i, (}
- FIRST(T') = {*, /, ε}
- FIRST(F) = {i, (}
- FIRST(A) = {+, -}
- FIRST(M) = {*, /}

FOLLOW集：

- FOLLOW(E) = {$, )}
- FOLLOW(E') = {$, )}
- FOLLOW(T) = {+, -, $, )}
- FOLLOW(T') = {+, -, $, )}
- FOLLOW(F) = {*, /, +, -, $, )}
- FOLLOW(A) = {i, (}
- FOLLOW(M) = {i, (}

然后，我们可以构造预测分析表。

| | i | ( | ) | + | - | * | / | $ |
|---|-----|-----|-----|-----|-----|-----|-----|-----|
| E | TE' | TE' | | | | | | |
| E'| | | ε | ATE'| ATE'| | | ε |
| T | FT' | FT' | | | | | | |
| T'| | | ε | ε | ε | MFT'| MFT'| ε |
| F | i | (E) | | | | | | |

最后，我们可以编写LL(1)语法分析程序。以下是Python代码实现：

class LL1Parser:
    def __init__(self, grammar):
        self.grammar = grammar
        self.table = self.construct_table()
    
    def construct_table(self):
        table = {}
        for i, production in enumerate(self.grammar.productions):
            X = production.left
            alpha = production.right
            first_alpha = self.grammar.first(alpha)
            follow_X = self.grammar.follow(X)
            for terminal in first_alpha:
                if terminal != "epsilon":
                    table[X, terminal] = i
            if "epsilon" in first_alpha:
                for terminal in follow_X:
                    table[X, terminal] = i
            if "epsilon" in first_alpha and "$" in follow_X:
                table[X, "$"] = i
        return table
    
    def parse(self, input_tokens):
        stack = ["$", self.grammar.start]
        input_tokens.append("$")
        input_pos = 0
        while stack:
            top = stack.pop()
            if isinstance(top, Symbol):
                if top == input_tokens[input_pos]:
                    input_pos += 1
                else:
                    raise Exception("Error: unexpected token '{}'".format(input_tokens[input_pos]))
            elif (top, input_tokens[input_pos]) in self.table:
                production = self.grammar.productions[self.table[top, input_tokens[input_pos]]]
                for symbol in reversed(production.right):
                    stack.append(symbol)
            else:
                raise Exception("Error: unexpected token '{}'".format(input_tokens[input_pos]))
        return True

该程序接受一个文法对象作为输入，并且在初始化时构造预测分析表。它还实现了一个parse方法，该方法接受一个输入符号串，并返回True或抛出异常。