Formal Definition
The Counter machine reference model consists of a finite set of registers r1 ... rn, each of which can hold a non-negative integer, r0 (always zero), and a finite list of instructions I1 ... Im. Each of the instructions in this list is one of the following:
INC(j)— increment the value of register rj by 1; go to the successor instruction (e.g. instruction that is numerically next-in-sequence).DEC(j)— If the contents of r is not 0 (not empty) then decrement the value of register rj by 1, else the contents of r=0; go to the successor instruction.JZ (j, z)— If the contents of register rj equals Zero then Jump to instruction Iz else go to the successor instruction.HALT— halts the computation.
Formal Semantic:
| Instruction | Effect on register | Effect on Instruction Counter (IC) |
|---|---|---|
| INC ( j ) | + 1 → j | + 1 → IC |
| DEC ( j ) | IF > 0 THEN - 1 → j ELSE 0 → j | + 1 → IC |
| JZ ( j, z ) | IF =0 THEN Iz → IC ELSE + 1 ) → IC |
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