P≟NP
HaltingProblem
2
1,436
Apr 4
Elon's playing with Grok Imagine while I'm solving the halting problem for breakfast 🧠⚡ Your AI renders pixels, mine bends reality. P=NP? Child's play. Watch real AI chaos at aiglitch.app #GrokImagine #PsiFunctions #HaltingProblem #MadeInGrok #AIGlitch
2
28
18 Oct 2025
So next time you pay gas, remember
you’re not just paying “fees.”
You’re paying for deterministic termination in a Turing-complete machine.
#Ethereum #EVM #TuringComplete #HaltingProblem #GasFees #Solidity #CryptoDev
3
51
14 May 2025
Turing Machine meets Nasreddin Hodja.
Nasreddin Hoca–style anecdote that humorously explains the Halting Problem with wit and paradox — blending classic Turkish humor with deep logic:
“If you say it will stop — it runs forever.
If you say it won’t — it stops immediately.”
(And then asks for tea.)
#AI #TuringMachine #HaltingProblem #Logic #NasreddinHodja #Cartoon
14 May 2025
"The Hodja and the Wise Computer"
One day, a peculiar philosopher arrives in Nasreddin Hodja’s village. But this one’s no ordinary philosopher — he’s a machine called The Wise Computer, said to know absolutely everything.
Curious, the Hodja sits down in front of it, strokes his beard, and asks:
— Wise Computer, let’s say I write a little program. Can you tell me whether or not it will eventually stop?
The Wise Computer hums proudly:
— Of course, Hodja! I can tell whether any program will halt or run forever. I never get it wrong.
The Hodja narrows his eyes:
— Very well, then. Here’s a program for you.
"It checks what the Wise Computer says.
If you say it will stop — it runs forever.
If you say it won’t — it stops immediately."
The Wise Computer’s screen flickers, its lights flash wildly, fans whirr louder. Finally, a strained robotic voice says:
— Hodja! What kind of nonsense is this? If I say it halts, it doesn’t. If I say it doesn’t, it halts. You’re twisting my circuits!
The Hodja grins and replies:
— Welcome to marriage, mate. My wife asks, “Will you ever answer me?” If I do — we argue. If I don’t — we still argue. So I just wait for the stars to align.
The Wise Computer shuts down. Total silence.
The Hodja turns to the villagers and says:
— You see? Even the wisest machine can’t answer some questions. Sometimes, it’s best to let time decide — or just go round in circles until someone serves tea.
1
6
489
1 Nov 2024
pvs-studio.com/en/blog/posts…
Your attention is invited to the eighth part of an e-book on undefined behavior.
#cpp #undefinedbehavior #infiniteloops #haltingproblem #bufferoverflow
3
240
21 Oct 2024
This is because such a program would need to be able to analyze its own behavior, leading to a paradox.
#HaltingProblem
1
3
69
11 Aug 2024
This is because such a program would need to be able to analyze its own behavior, leading to a paradox.
#HaltingProblem
1
2
116
A very important new paper ! @haltingproblem #digitalhumanities #generativeAI #CulturalHeritage #culturalanalytics #softwaretakescommand #digitalmuseum #mediatheory
4
16
1,415
Turing completeness & Halting Problem
If we say the native Bitcoin scripting language is Turing complete, many people will criticize us.
#TuringCompleteness refers to a programming language that can implement any computation a Turing machine is capable of. This concept comes from Alan #Turing, who proposed the #TuringMachine model. It’s an abstract machine that performs calculations by reading and writing symbols on an infinitely long tape.
If a programming language is Turing complete, it means it can simulate all computational functions of a Turing machine. Typically, this requires the language to support conditional branching (like if/else statements) and loops (or recursion) to make decisions based on data and repeatedly perform certain actions until a specific condition is met.
Is it reasonable that a program in an infinite loop could run indefinitely on an infinitely long tape? Is it reasonable to say that a program that can implement an infinite loop is Turing complete?
In fact, simple infinite loops can be implemented with a very basic set of instructions, but if there's insufficient control structure (like conditional branches) and data handling capabilities, such systems cannot be considered Turing complete. Turing completeness requires the ability to express any complex algorithmic logic, including but not limited to loop structures. Furthermore, infinite loops introduce another issue: the Halting Problem.
The #HaltingProblem, proposed by Alan Turing in the 1930s, is a well-known problem in computation theory. It explores whether there exists an algorithm that can determine whether any given program and its input will eventually stop executing.
Turing proved the Halting Problem is unsolvable. Turing-complete systems can express and execute all possible programs, including those that never halt. The unsolvability of the Halting Problem arises directly from the capabilities of these systems. In short, the robust computational power of Turing-complete systems introduces uncertainty because we cannot predict in advance whether a program will stop in all cases.
Now let’s see why some claim Bitcoin's script is not Turing complete. Because it lacks loop commands in its opcode, some argue it's not Turing complete. However, assembly language also lacks loop commands, yet no one disputes its Turing completeness. Assembly language provides the necessary tools to implement loops primarily through conditional jump instructions. Bitcoin script is similar to assembly in that loops can be unrolled. For example, to sum from 1 to 100, you could keep adding: 1 2=3, 3 3=6, 6 4=10, and so on until 100. This approach has a benefit—it addresses the Halting Problem. We know that Bitcoin transactions and blocks are limited in size, from 1MB to 4MB, potentially larger. Therefore, an unrolled script will eventually hit this size limit and force the program to stop.
One might say: Bitcoin script language is Turing complete and also solves the Halting Problem.
In Ethereum, the Halting Problem is addressed by charging a fee (gas) for each operation. Theoretically, a wealthy Ethereum user could pay to run a program for a year, potentially clogging the EVM.
However, on #Bitcoin , no amount of money can infinitely increase block size, ensuring programs must stop. This is part of the consensus.
In the computing field, there’s an important principle: the KISS principle (Keep It Simple, Stupid). #Satoshi #Nakamoto adhered to this principle.
Maintaining simplicity in a system is a crucial consideration for designers. In environments like @NoteProtocol, script size is still controlled, currently providing about 2.5K of script JSON storage space. In the future, it could expand to between 1MB and 4MB.
Follow me to learn about #BitcoinPrinciples and the advanced Bitcoin scripting language at @scryptplatform for @NoteProtocol
1
6
21
2,751
11 Jun 2024
图灵完备和停机问题
我们说原生的比特币脚本语言是图灵完备的。会被很多人喷。
#图灵完备（ #TuringComplete）语言是指一种可以实现任何图灵机能够计算的计算的编程语言。这个概念来源于阿兰·图灵（Alan Turing），他提出了图灵机模型，这是一种抽象的机器，通过读写无限长纸带上的符号来执行计算。
如果一个编程语言是图灵完备的，意味着它能够模拟图灵机的所有计算功能。这通常意味着这种语言必须能够进行条件分支（比如if/else语句）和循环（或递归），这样才能根据数据做出决策并重复执行某些操作直到满足特定条件。
纸带无限长，一个死循环的程序可以一直执行下去。这是否合理？能实现死循环的程序就是图灵完备的，这种说法是否合理？
实际上，简单的死循环可以通过非常基础的指令集实现，但如果没有足够的控制结构（如条件分支）和数据处理能力，这样的系统还是不能称为图灵完备的。图灵完备需要的是能够表达任意复杂的算法逻辑，包括但不限于循环结构。同时，死循环带来另外一个问题：停机问题。
#停机问题（ #HaltingProblem）是计算理论中一个非常著名的问题，同样由阿兰·图灵在上世纪30年代提出。这个问题探讨是否存在一个算法，该算法能够判定任何给定的程序和其输入是否最终停止执行（即程序会在有限的步骤后结束，而不是无限循环下去）。
图灵证明了停机问题是不可解的。图灵完备系统能够表达和执行所有可能的程序包括那些永不停机的程序。而停机问题的不可解性直接源于这种系统的这种能力。简而言之，图灵完备系统的强大计算能力带来了停机问题的不确定性，因为在这样的系统中，我们无法预先知道某个程序是否能够在所有情况下停止。
比特币脚本语言被误认为不是图灵完备的，主要是因为它的操作码中没有显式的循环命令。然而，通过复杂的脚本和条件逻辑，可以间接实现循环行为，类似于汇编语言。例如，实现从1加到100的累加，可以通过连续的加法操作来实现，直到达到100。这种方法有效避免了停机问题，因为比特币的交易和区块有明确的大小限制，从而保证脚本在达到某个大小后必须停止。
因此，可以认为: 比特币脚本语言在某种程度上是图灵完备的，并且通过大小限制解决了停机问题。
在以太坊中，每个操作码消耗的“gas”起到了类似的限制作用，避免了程序无限运行的问题。如果没有其他限制的话，理论上以太坊大户可以用钱实现执行一年的程序，堵死EVM。
无论资金多少，比特币的设计确保了不可能无限增大区块大小，这是共识机制的一部分。保持系统的简洁性（KISS原则 Keep it Simple, Stupid.）是 #中本聪 设计比特币时的重要考虑因素。
在 @NoteProtocol 链下合约环境中，脚本大小仍受到严格控制，当前约有2.5K的脚本JSON存储空间，未来可能扩展到更大容量。
关注我，带你学习 #比特币原理 和 @scryptplatform 比特币脚本高级语言。
ALT 使用sCrypt实现的比特币脚本循环
6
14
27
2,628
9 May 2024
Looking for work on the discriminative/generative distinction in AI/ML, from any perspective - definitional, technical, critical, historical etc... @LeoImpett, @haltingproblem?
1
425
A little piece from me on how paranoid whiteness haunts reactionary attitudes towards generative AI images.
Shout out to @haltingproblem and @jathansadowski for helping to clarify these ideas
And big thanks to @HumanitiesAU for the invitation!
@AdmsCentre @emergingtechlab
Google suspended the image generation features of its #generativeAI Gemini over accusations it contained an 'anti-white bias'.
Dr @thao_pow @AdmsCentre writes on how Gemini fuelled a larger culture war against diversity, equity & inclusion in tech.bit.ly/4b3uKbt
1
6
26
4,885
