My son has been playing Little Big Planet 2 lately, and I noticed that the game editor allows AND gates, OR gates and NOT gates... Is it Turing complete? If so, can anyone recommend a source for learning to turn those primitives into something like a higher level conditional if?
You need NOT and one of AND or OR to be able to do all binary logic. This is DeMorgan's Law, basically.
However, this is not sufficient for Turing completeness. For that you also need random (or reducably equivalent) access (theoretically) infinite memory.
Odds are, you'll be able to build a flip flop (a D flip flop is built using NANDs, so its easy) using the available logic gates. From those, you can build a register, and with enough of those you'll be equipped to build some simple programs.
A nand gate is all that is required, everything can be built from that, so the three you have are plenty. Here's a course that takes you from logic gates, up through building a computer, all the way to writing an operating system: The Elements of Computing Systems: Building a Modern Computer from First Principles
An idea: you should be able to construct a NAND gate, so you can then build a XOR gate. With XOR and AND you can build a half-adder. Combine half-adders to build a full-adder. That would be a start at least.
NAND and NOR are basic building blocks for other gates so chances are Turing completeness is just around the corner.
AND, OR and NOT is functionally complete, that is, all possible truth tables can be expressed. Which I believe also makes it turing complete, since you can construct a general purpose processor with any functionally complete set of gates
I'm know I'm late to the game here but yes. I play LBP2, and it has an AND, OR, NOT, XOR, NAND, NOR. You can also add and subtract signals, there is also ways to do binary in the game.
The only gates you need are NOT and OR. With those two you can build all other logic gates. For example, NOT(OR(NOT|NOT)) is an AND gate, OR(NOT|NOT) is NAND, NOT(OR()) is NOR, etc. The difficult one to make (and also most functionally useful) is XOR, which can be made with a tree of NAND gates, which in turn can be made with NOT and OR as shown above.
来源：https://stackoverflow.com/questions/4908893/what-logic-gates-are-required-for-turing-completeness