Why does it matter if it’s a 16-bit cpu, a 32-bit cpu, or 64-bit? For example, what can a 64-bit cpu do that a 32-bit one can’t? Or otherwise, and can you tell the difference when you casually use a computer?

What I mean is 1080p has 2,073,600 pixels so what if every single pixel is run by a individual PC like 2,073,600 PCs?

I was thinking this might be a way to create a super-computer that can put out a insane amount of framerate.

In light of the recent counterproof of the Jacobian Conjecture, I've been looking more into proofs, and I can't wrap my head around how Lean works. In my mind, proofs always require a certain amount of intuition and judgement behind them, so I'm confused how a deterministic programming language can infer from said proofs?

Wait-Free means that every thread must finish its operation in a bounded number of steps. That bound can be arbitrarily high, e.g. dependent on the number of concurrent threads, but it must be finite. And the finite bound must be there in all cases, i.e. it is not sufficient to say that an algorithm "usually" finishes "reasonably" (i.e. "usually" does not spend unbounded times helping other threads).

The first practical implementation of a multiple-enqueuer multiple-dequeuer Wait-Free Queue was proposed by Kogan and Petrank. The key idea is that threads help each other, but in a way that newer threads (more precisely: newer operations) are obliged to help older threads (operations), but not vice versa. Also, plainly said: If a thread cannot make progress with its own operation, it becomes older and older, up to the point when all other threads are obliged to help (only) him, thus ensuring the Wait-Free progress.

The issue of the Kogan and Petrank Queue is, however, that it is based on a linked list of nodes. This means that its operations constantly produce memory churn, also require memory allocation and memory clean-up. From Java - where the clean-up is done by a Garbage Collector - I borrow the term "Garbage".

Now, the problem is that Wait-Free memory allocation is problematic. Imagine, e.g., when the process needs a new memory page from the operating system. Can this ever be made Wait-Free?

Memory reclamation in a concurrent setup is a complex topic on top of that. One of the key questions here is: When can a memory block be freed safely, i.e. how do we "know" that no thread has a pointer to it anymore?

Given this, it appears that one needs a structure without memory churn (i.e. Garbage-Free) to be able to make it Wait-Free. At least practically.

I would be grateful for a discussion on this.

Additional info:

Here I have combined the Multi-Array Queue (which is Garbage-Free by nature (except of the extension operations, of course)) with the Kogan and Petrank idea, with the aim to obtain a Queue that is Wait-Free unconditionally.

The GitHub repo also contains a visual simulator to illustrate the principle:

https://github.com/MultiArrayQueue/WaitFreeMultiArrayQueue