Re: On infinite recursion, SHDs and the halting problem

On 2025-05-20 18:47:06 +0000, Mr Flibble said:

It is sufficient for an SHD to DETECT infinite recursion without having to
SIMULATE it.  Indeed this has to be the case given that an SHD, like any
decider, must furnish a decision in FINITE time.
 This is consistent with Flibble's Law:
 If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.

If you want to permit infinte behaviour for decidability you need to
define how an infinite behaviour specifies a decision. With finite
and hyperfinite behaviour one can use the final state or the final
content of the tape but neither is there if there is no last state.
--
Mikko