You know, it has not actually been demonstrated that human consciousness can be mimicked by Turing-equivalent computer.
The evidence is extremely strong that human minds are processes that occur in human brains. All known physical laws are Turing computable, and we have no hint of any sort of physical law that is not Turing computable. Since brains are physical systems, the previous two observations imply that it is highly likely that they can be simulated on a Turing-equivalent computer (given enough time and memory).
But regardless of that, the Sleeping Beauty problem is a question of epistemology, and the answer necessarily revolves around the information available to Beauty. None of this requires an actual human mind to be meaningful, and the required computations can be carried out by a simple machine. The only real question here is, what information does Beauty have available? Once we agree on that, the answer is determined.
The evidence is extremely strong that human minds are processes that occur in human brains. All known physical laws are Turing computable, and we have no hint of any sort of physical law that is not Turing computable. Since brains are physical systems, the previous two observations imply that it is highly likely that they can be simulated on a Turing-equivalent computer (given enough time and memory).
But regardless of that, the Sleeping Beauty problem is a question of epistemology, and the answer necessarily revolves around the information available to Beauty. None of this requires an actual human mind to be meaningful, and the required computations can be carried out by a simple machine. The only real question here is, what information does Beauty have available? Once we agree on that, the answer is determined.