What logic gates are required for Turing completeness?

Question

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 recom

Answer 1

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.