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Counter Machines

Counter machine has the same structure as the multi-stack machine but in place of each stack is a counter. Counters hold any non-negative integer,but we can only distinguish between zero and nonzero counters. That's the move of the counter machine depends on its state,input symbol and which if any of the counters are zero. In one move,the counter machine can
a)change state
b)Add or subtract 1 from any of its counters,independently. However a counter is not allowed to become negative,so it cant subtract from a counter that is currently 0.

 Counter Machine may also be regarded as a restricted multi-stack machine. The restrictions are as follows,
a)There are only two stack symbols,which we shall refer to as Z0(the bottom of stack marker) and X.
b)Z0 is initially on each stack.
c)We may replace Z0 only by a string of the form X^iz0 for some
   i >=0.
d)We may replace X only by X^i for some i >= 0. That's Z0 appears  
only on the bottom of each stack and all other stack symbols if any are X.

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