Good Day,
I would like to ask this question. Infinite Time Turing Machine ordinals are countable ordinals. Also I have read that ITTM either halts or repeats itselve after countably many steps.
Does that mean that ITTMs are not able of doing hypertask, which is defined as doing uncountably many computational steps in finite time (by uncountably many I mean the cardinality of Reals so assume Continuum hypothesis is true)?
Also If that is true, may I ask you of some kind of problem (other than halting problem for ITTMs) that ITTMs would not be able to solve but hypercomputer capable of hypertask would be able to solve?
Thank you very much for your kind answers.
EDIT: Maybe the question is better asked this way: Lets have hypercomputer capable of doing ℵ1 operations in finite time, where those operations are equivalent with operations that CISC cpu can do. This machine can take input with maximum length of ℵ1 bits and can take programs with length at most ℵ1 bits. Is this hypercomputer more powerul then ITTM? What kind of problems could it solve that ITTM could not?