Incrementing machine

Incrementing machine is a variation of Minsky machine discovered by User:ChuckEsoteric08. Unlike any other counter machines it can only increment registers, but not decrementing or setting them to 0. It was discovered while author was working on Turing-completness proof for AddJump

Specification

Incrementing machine uses unbounded amount of registers as memory which are numerated with the first register being 0, second being 1 and so on. All of them are initially set to 0. Commands look like this:

<label> <counter1> <counter2> <branch>

It is executed as follows: increment register <counter1> and if result is equal to <counter2> then jump to label <branch>

Computational class

Incrementing machine is Turing-complete since it can implement Counter machine with following instructions:

INC x y - Increment counter x and jump to line y
DEC x y - Decrement counter x and if result was 0 jump to line y

If a command has only one argument, it means that it would jump to the next command
Which can simulate Minsky machine JZDEC x y insturction like that:

INC x
DEC x y
DEC x

Each counter is represented as two Incrementing machine counters, called a and b. INC insturction is simulated like that:

<line number> a a y

DEC instruction is simulated like that:

<line number> b a y

Where y is the line to which it should jump to. It will also prove that it needs only 4 counters to be Turing complete

Implementations

The following Python script is an interpreter.

prgm = [[]]
prgm.pop(0)
while True:
    line = input('%s ' % len(prgm)) # Generates labels automatically
    if line != "eof":
        line = list(line.split(" "))
        prgm.append([int(line[0]), int(line[1]), int(line[2])])
    else: break
tape = [0]
for i in range(0, 256): # Expansion is trivial
    tape.append(0)
# Executes the program
def incmac(label, counter1, counter2, branch):
    global tape
    global inst
    tape[counter1] += 1
    if tape[counter1] == tape[counter2]:
        inst = branch
    else: inst += 1
    print(tape[counter1], end=" ") # For debugging
inst = 0
while inst < len(prgm):
    incmac(inst, prgm[inst][0], prgm[inst][1], prgm[inst][2])

256-cell implementation, but it can be expanded.