I don't know this field very well so I might be misunderstanding, but I think this is different than "infinite tape" in Turing Machines. As I understand it, the proof of universality for Rule 110 required that the program code which is called the "production rules" be repeated infinitely on the tape even for a finite size program. https://en.wikipedia.org/wiki/Rule_110#:~:text=An%20infinite...
If you had a halting problem oracle to tell you how much runtime is needed to run a certain program to completion, you could get away with having only a finite number of repetitions of the "production rules", and simply pretending that they're infinitely repeated. This would only work for programs that halt.
If I understand correctly, any program that loops forever, if implemented within Rule 110 Cyclic Tags, requires infinite repetition of the production rules. I think this is a difference of Rule 110 vs Turing Machine tape. If I understand correctly, a Turing Machine with finite, even quite small, tape can loop forever. But a Rule 110 program must have infinitely sized tape to be able to loop forever.
Basically (if I understand correctly), Rule 110 Cyclic Tags essentially "consume" tape symbols as basically a non-renewable resource, like an electrical computer server powered by the burning of coal. Infinite runtime (looping forever) requires infinite repetition of the tape symbols (both the "production rules" and the "clock pulses" - see the Wiki page above). I believe this is unlike Turing Machines, which can loop forever without "consuming" any non-renewable resource.
To clearly state this again: Running a simple "while(true)" loop in a Turing Machine only needs finite tape, but requires infinite tape in Rule 110.
Whereas the Rule 110 Cyclic Tags engine requires the infinite tape to contain infinite repetitions of structured patterns, even in order to simply run "while(true)". That's a key difference.
Oh, I see what you mean. That sounds quite easy to work around, actually. Due to the speed of light, only a section containing the disruptions to the repeated pattern need be considered for the initial state; and then you can compute outward from that.
"Allowed" is probably covering too wide a meaning in your description. Just because something is capable of defining infinite consumption does not mean it was allowed to do so in the proof.
If you had a halting problem oracle to tell you how much runtime is needed to run a certain program to completion, you could get away with having only a finite number of repetitions of the "production rules", and simply pretending that they're infinitely repeated. This would only work for programs that halt.
If I understand correctly, any program that loops forever, if implemented within Rule 110 Cyclic Tags, requires infinite repetition of the production rules. I think this is a difference of Rule 110 vs Turing Machine tape. If I understand correctly, a Turing Machine with finite, even quite small, tape can loop forever. But a Rule 110 program must have infinitely sized tape to be able to loop forever.
Basically (if I understand correctly), Rule 110 Cyclic Tags essentially "consume" tape symbols as basically a non-renewable resource, like an electrical computer server powered by the burning of coal. Infinite runtime (looping forever) requires infinite repetition of the tape symbols (both the "production rules" and the "clock pulses" - see the Wiki page above). I believe this is unlike Turing Machines, which can loop forever without "consuming" any non-renewable resource.
To clearly state this again: Running a simple "while(true)" loop in a Turing Machine only needs finite tape, but requires infinite tape in Rule 110.