Single Instruction URM Programs/Zero Function
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Theorem
The zero function $\Zero: \N \to \N$, defined as:
- $\forall n \in \N: \map \Zero n = 0$
is URM computable by a single-instruction URM program.
Proof
The zero function is computed by the following URM program:
Line | Command | |
---|---|---|
$1$ | $\map Z 1$ |
This sets the value $0$ into $R_1$ and then stops.
The output $0$ is in $R_1$ when the program terminates.
$\blacksquare$