What about parallelism?
This made me facepalm. What about it? These physicist used the laws of thermodynamics to establish a fundamental limit to how much usable information can be inserted or extracted from a volume of space. What does parallelism have to do with that at all? What indeed?
See how easy it is to ask rhetorical questions?
I'm not sure that I want the same pool of people that believe in faces on Mars, and other hoaxes, interpreting photos of North Korea.
I just thought of a simple proof that the halting problem does not apply to Turing Machines with finit e memory (which means it isn't really a Turing Machine, but oh well).
The input of a Turing machine is the initial contents of the tape. Therefore a Turing Machine with finite memory only has a finite number of possible inputs. It is possible for me to simply go through all those possible inputs and mark them as "Accept" or "Reject". Since it is not possible (through diagonalization) to construct an input that is not in my list, I have accounted for every possible input. I can implement HALT by simply consulting my table. All possible finite memory Turing machines and their inputs can be constructed this way, so HALT is implementable for a Turing machine with finite memory.
QED motherfucker.
But the proof depends on not being able to know if the Turing machine is done or not. A Turing machine with finite memory does not have that problem.
I just gave you a proof. It wasn't formal, but it covered all the cases.
Given a Turing machine with a finite memory and an input it will either halt (accept or reject), eventually enter a state it has been in before (infinite loop, so reject), or attempt to enter a state that requires more memory than it has (we can take that as a "reject"). Therefore it is possible to know if the machine accepts or rejects in all cases.
This cannot be practically applied because the amount of space and time required even for small machines is still too large but it does make the point that the halting problem depends on the infinite nature of the Turing machine.
You will never find a programming language that frees you from the burden of clarifying your thoughts.
http://www.xkcd.com/568/
It is pretty obvious that they intend to send time travelers to the exact point in time and space that the pirate was recording and arrest them.
Either that or open up a wormhole and bring them to the future for justice.
Maybe just sent a telegram back in time to alert the past. But that is not as fun.
What is algebra, exactly? Is it one of those three-cornered things? -- J.M. Barrie