TDQ

TDQ (or Turing DQ) is an extension of DQ created by User:ChuckEsoteric08.

Additions

Operations are now executed in sequential order. There are now four stacks, which could be seen as registers. Registers are named a, b, c and d. Command D has changed it's meaning since it was equivalent to 1.

Command	Description
xy	execute command y on stack y. If there is no x then it would be executed on stack a. It is counted as a single instruction
*x	if length of stack x is not equal to the next stack (so that a is compared to b, b to c d to a) skip next instruction
D	jump to 1-indexed line n, where n is represented in unary as a string of D's.

Computational class

It is Turing-complete, which can be proven by translating Minsky machine with two registers (0 and 1) into it

Minsky machine syntax

INC x Lx

Increment x and jump to instruction Lx

JZDEC x Lx Ly

If x is zero jump to line Lx, else decrement it and jump to Ly

Translation

INC 0 Lx =
 1DLx
INC 1 Lx =
 c1DLx
JZDEC 0 Lx Ly =
 *aDLxb1DLy
JZDEC 1 Lx Ly
*cDLxd1DLy

Where

Dx

Represent string of D's with a length of x