I don't have a confirmed case of Linux running without a traditional CPU, but I wouldn't bet $20.00 against it existing
There's plenty of devices out there that do some kind of computation and don't have anything we would recognize at a traditional CPU. Such devices are becoming rare, because CPUs are so dang cheap, now.
Most of those run binary compiled from custom C code or even directly from Assembly.
But, if someone was going to run an alternative program on one of those devices, there's a very good chance they would install Linux (heavily customized) on it first.
Source: I've completed parts of Linux from Scratch. It was eye opening to realize the places that a true Linux expert could get it to run. Every single part of Linux is truly optional, to someone who knows that they're doing.
Good. Because if Linux can run on RV32I, then it can run on this.
Every single part of Linux is truly optional, to someone who knows that they're doing.
Today for shits and giggles I ran Xonotic as init process. It had trouble with hardware acceleration, so I ran simple bash script that mounted /proc and /sys and then launched xonotic instead.
It literally says "32 bit RISC-V homemade CPU out of discrete components".
I dont know how you would stretch the definition of cpu in form of discrete components but yea current processors also stray from the definition of a alu and a control unit and registers since people call the different cores cpus. But even a Mikrocontroller has a all that.
You need a cpu to run linux. If you just want to rin a "program" you can do that with logic gates and no alu or control unit but that would limit the form of your program to exactly that circuit.