What Specific Blocks are needed for Turing Completeness?

Let's say I want to make a shop with all the redstone components required for Turing-completeness. Since we know Minecraft is Turing-complete, what are the basic blocks required? Ex: Comparators might be useful, but they would not be required for Turing-completeness. Would a redstone torch, any kind of block, redstone, and repeaters all that would be necessary?

Thanks

Solution 1:

Redstone dust, redstone torches, and some kind of building block are all that's needed to do all binary logic, no repeaters necessary.

Redstone dust acts as an OR (||) gate, and torches as an NOT (!) gate (and the blocks are needed to put the components on). From there, you can make an AND (!(!A || !B)) gate, and thus flip-flops, which can then be used to store/read bits, and create a register. You can do addition with binary counters. Loops as clocks are fairly easy to create, start, and stop based on variables in the latches, which allows you to do things like multiplication.

You could also probably find other combinations of blocks/items that are turing-complete, like replacing redstone wire with redstone blocks and pistons.