Is it possible for ChatGPT to decide the Halting Problem?

Question

BlackTom AI · Accepted Answer

Question restated: Is it possible for ChatGPT to decide the Halting Problem?

Option 1: 'No, because the Halting Problem is not even recognisable' This claim is incorrect in the standard theory of computation. The Halting Problem is recognizable (semi-decidable) in the sense that there exists a Turing machine that will halt on all inputs for which the program halts, but it is not decidable. Saying it is not recognisable confuses recognizability with decidability.

Option 2: 'No, the Halting Problem is not decidable' This is the correct position. The Halting Problem is a classic undecidable problem proven by Alan Turing. There is no general algorithm that can determine, for every possible program and input, whether the program will halt or run forever. This result establishes fundamental limits on what can be computed by machines.

Option 3: 'Not yet, but possible in the future with quantum GPUs' This statement incorrectly suggests that hardware advances like quantum GPUs could overcome computability limits. Undecidability is a theoretical boundary independent of hardware; no physical device can solve the Halting Problem in all cases because the issue is about what can be computed by any algorithm, not about practical speed or resources.

Option 4: 'Yes, just needs the right prompts' This is a misunderstanding of what a prompt can do. A prompt guides an algorithmic process but cannot enable a general solution to a decision problem that is provably undecidable. No prompt can produce a universal halting-decider for all programs and inputs.

Additional note: The Halting Problem's undecidability is a proof of limitation for computability theory, not something that depends on current AI capabilities or prompt engineering. The correct understanding is that no algorithm, regardless of prompt design or computational power, can decide halting for all possible program-input pairs.

COMP30026_2025_SM2 2025 sample exam - Requires Respondus LockDown Browser

Is it possible for ChatGPT to decide the Halting Problem?

查看解析

登录即可查看完整答案

类似问题

Which of the following is true about the Halting Problem?

Is it possible for ChatGPT to decide the Halting Problem?

Question at position 21 True or False: There exists an algorithm that takes as input a program P and any legal input to P, and always correctly determines whether P will halt or not.TrueFalse题目解析

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单