停机问题为什么不可解？
Why is the halting problem unsolvable?
假设存在能判断‘任意程序是否停机’的机器 H，就能构造一个利用 H 自相矛盾的程序，使 H 既必须停又必须不停。因此这样的 H 不可能存在。
If a machine H could decide whether any program halts, we could build a program that uses H on itself to contradict—forcing H to halt and not halt. So such an H cannot exist.
难度 专业 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
Cook《The complexity of theorem-proving procedures》（1971，STOC）；Sipser《Introduction to the Theory of Computation》
Cook, The complexity of theorem-proving procedures (1971, STOC); Sipser, Introduction to the Theory of Computation
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL19859284W：Introduction to the th
#图灵 #不可判定
图灵机是什么概念？
What is the concept of a Turing machine?
它是一种抽象计算模型：一条无限纸带加一个按规则读写的头，能模拟任何‘算法’。它定义了‘可计算’的边界。
It is an abstract model of computation: an infinite tape plus a head that reads/writes by rules, capable of simulating any 'algorithm'. It defines the boundary of what is computable.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
Cook《The complexity of theorem-proving procedures》（1971，STOC）；Sipser《Introduction to the Theory of Computation》
Cook, The complexity of theorem-proving procedures (1971, STOC); Sipser, Introduction to the Theory of Computation
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL19859284W：Introduction to the th
#图灵 #可计算
图灵在二战中破了什么密码？怎么做的？
What code did Turing break in WWII, and how?
他帮助破译德军的恩尼格玛（Enigma）密码机。他设计电磁‘炸弹机’（Bombe）利用已知明文和机器结构快速搜索每日密钥，大幅缩短破译时间。
He helped break the German Enigma machine. He designed the electromechanical 'Bombe' that exploited known plaintext and the machine's structure to search daily keys fast, slashing decryption time.
难度 进阶 · 适合 小学高段(9-12)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：本题原挂出处与答案内容不符，已撤回；具体书目待补，暂不展示来源。
本题原挂出处与答案内容不符，已撤回；具体书目待补。
Previous citation withdrawn as unsupported for this answer; a specific source is pending.
#图灵 #密码