1.3 KiB
1.3 KiB
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| 2024-2025学年下学期期末 |
2025春季学期计算理论基础期末考试试卷（回忆版）
注：这次考试的形式是五道题自行选四个做, 每题25分, 多做没有加分；此外, 原卷面是英文, 请大家注意
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给出接受以下语言的DFA:
所有以1开头, 能被5整除的二进制串, 如101, 1010, 1111, 左侧（自动机读入的第一个符号）为最高位, 右侧为最低位 -
请给出 DFA 化简中 State Elimination Technique 的复杂度的 tight bound, 要有明确的推理过程
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A marble is dropped at A and B. Levers x1, x2 and x3 cause the marble tofall either to the left or to the right. Whenever a marble encounters a lever, it causes the lever to reverse after the marble passes, so the next marble will take the opposite branch. The game wins when there is a marble falls through C. The levers are all initialized to the left. Model this toy by a DFA.
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证明语言
L = \{a^nb^nc^md^m (n \geq m \geq 1) \cup a^nb^mc^md^n (n \geq m \geq 1)\}不是 CFL -
构造如下的图灵机, 其功能为：给定三个非负整数
n, m, k, 判断n + m是否等于k.输入的形式为：
$\underbrace{11……1}_\text{n个}0\underbrace{11……1}_\text{m个}0\underbrace{11……1}_\text{k个