Clear Registers Program
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URM Program
Let $a, b \in \N$ be natural numbers such that $0 < a$.
Then we define the URM program $\map Z {a, b}$ to be:
Line | Command | |
---|---|---|
$1$ | $\map Z a$ | |
$2$ | $\map Z {a + 1}$ | |
$3$ | $\map Z {a + 2}$ | |
$\vdots$ | $\vdots$ | |
$b - a + 1$ | $\map Z b$ |
where $\map Z a$ denotes the zero instruction:
- $r_a \gets 0$
Hence this URM program zeroizes all the registers from $R_a$ through to $R_b$.
If $a > b$ then $\map Z {a, b}$ is the null URM program.
The length of $\map Z {a, b}$ is:
- $\map \lambda {\map Z {a, b} } = \begin {cases}
0 & : a > b \\ b - a + 1 & : a \le b \end {cases}$
Proof
Self-evident.
$\blacksquare$