User:Taneb/Lowgate and Dilston

Lowgate and Dilston are two different languages that are related in that they can only be Turing-complete if Collatz conjecture is false. If the Collatz conjecture is false, at least one of these languages is Turing-complete (although not necassarily both).

Lowgate

Lowgate is Turing-complete if and only if an infinite trajectory occurs.

Memory is stored in an indexed tape of integers bounded to an implementation-dependent degree that wrap around, with a pointer P. P is an unbounded positive integer. Also there is another variable called Q which is similar to to P. [P] is shorthand for the tape element at index P.

The first line of input is the initial value for P and Q, beyond which commands are as follows:

Header text	Header text
>	Set P to Collatz(P)
+	Increment [P]
@	Swap P with Q
v	Set Q to P
[	If [P] is 0, skip to the matching ]
]	If [P] is not 0, go back to the matching [

Dilston

Dilston is Turing-complete if and only if a non-trivial loop occurs.

Coming soon!