Slashdot Mirror
A Model Railroad That Computes
tri44id writes "Several blogs have noted an Austrian team that has built a model train set that is a primitive computer. I have to point out, though, that it's actually only a Finite State Machine, like a pocket calculator, not a general-purpose device. Their plan for a general purpose layout is for an infinite-state machine, not a FSM+tape that Turing envisioned in his original paper. Turing took the concept a further step, by presenting a Universal Turing Machine that embodies a special set of states and transitions that allows its tape to be programmable to emulate any other TM. Do Slashdot readers know of any mechanical implementations of a truly Universal Turing Machine? (Danny Hillis' famous tinkertoy tic-tac-toe machine has neither infinite tape nor programmability, and is thus yet another FSM. It shouldn't be hard to elaborate the Austrian model train FSM to use a series of cars carrying movable magnets to represent Turing's tape cells writable with different symbols, and thus become a true TM or even UTM."
Turing machines. FSM
Did he inhale?
That is really awesome! The idea of a model railroad being a computer is not new though. I read a book by Desmond Bagley (or was is Alistair Maclean) many years ago where a scientist who wanted his work to remain secret built a model railroad/computer. His dying act is to give his model railroad timetables to the main character. The main character later realises that the timetables are actually code for this unique computer.
A Turing Machine is a simple model of computation that encompasses anything that can be computed by a computer. The strongest claim about the ability of a programming language is that it's "Turing Complete", which means that anything that can be computed on a Turing Machine can be computed in a language. Turing Machines are designed to be very simple, and they're good for theoretical things about computer science.
A Universal Turing Machine is a Turing Machine that takes, as its input, an encoding of another Turing Machine, then simulates it. As such, you can prove that with a Turing Machine, you can compute anything that any other Turing Machine can.
By contrast, Finite State Machines, or Finite Automata, are far less complex models of computation. If you treat them as language acceptors (i.e., everything that they compute is whether or not a string is valid in a language) they are only as powerful as simple regular expressions. They can be modelled very quickly by computers, though, since they are deterministic and require no lookahead.
I have to point out, though, that it's actually only a Finite State Machine, like a pocket calculator, not a general-purpose device
Yes, and your desktop computer is also another example of a finite state machine. Granted, all those little silicon switches have an enomorous number of possible states, but rest assured, the total number is indeed finite.
There was a 70s adventure novel - I believe by Hammond Innes although the title eludes my memory) in which a bomb-scientist who had promised to do no further research when he left government service is kidnapped
Investigators found that he had a large model railway which was controlled by a computer and the answers to calculations were reported by numbered wagons being arranged in certain orders and locations.....
It wasn't a very good book, actually.
I have been a user for about 10 years. This ends Feb 2014. The site's been ruined. I'm off. Dice, FU
A 'proper' Turing machine is supposed to be able to take on infinitely many states, OK?
That means that if you want to build one, before you get into how you are going to have the thing operate, you at least have to find a way of coding infinitely many discrete states using some finite amount of matter. Which is not possible: even if you could manipulate matter to the point of using every individual subatomic particle to store a bit of data, there are only finitely many particles and you will have a finite state machine.
Per the Heisenberg uncertainty principle, you cannot try to encode your state as an infinite-precision real which is (part of) the position or whatever of an object either, if you want to build a machine which is always contained in a finite space.
You could build a machine which will extend up to physical limits: stick a radar reflector in space, well away from any gravitational influence (which might be a problem, but...), and build a rocket ship which keeps track of how far away the radar reflector is, in the obvious way, keeps it an exact multiple of 1 metre, and runs a universal program (can do this in silicon logic on board) with that distance as the register. Assume that somehow it is possible to fuel the ship. With a bit of care, you can program things such that this program goes wrong with very low probability (you can allow for relativity, you can't rule out quantum effects deciding to move things suddenly by >0.5m, but it is very very unlikely). That will function as a universal Turing machine whenver you put in a program that does not require you to store any really large numbers. But when you are required to store large numbers you may run up against a physical limit in that you may well find there is an upper limit on the length of a geodesic in space-time, and you will be unable to store bigger numbers.
"billions of states" can be achieved with ~30 bits of memory.
I believe that in order to model "any physical computation device" you're going to need many many more states
(1KB RAM == 2^8192 states == ~1e2466 states).
You're trying to be clever but I hope you do know that having a "finite number of states" is not in and of itself a definition of a FSM. He wasn't trying to be clever, just accurate. Your computer is a finite state machine; It is not a Turing machine. We tend to think of them as Turing machines only because they have an enormous number of states; thus they seem to act like Turing machines as long as we don't do anything that requires more states than the computer has. However, when you run out of ram and/or disk space, you've just recognized the limitation of your desktop FSM. It is demonstrably the case that a finite state machine cannot be programmed to run a JVM or a Python interpreter. That is incorrect. Every computer program is a FSM.
The resulting computers are nondeterministic. They are computers in the sense that, given a Turing machine and a given input, you can construct a corresponding sliding-block puzzle that is solvable if and only if the Turing machine would eventually print YES. The catch is that this only works when the Turing machine is allowed to use only an amount of tape polynomial in its input size (but then, the same is effectively true of real computers). Technically, this means that sliding-block puzzles are PSPACE-complete - that's the next complexity class up from NP-complete.
Anyway, the construction does involve building logic gates out of sliding-block components, so the things are rather like actual computers. The constructions are based on the earlier result that you can build computers out of Rush Hour puzzles.
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