Definition:Trace Table
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This page is about Trace Table in the context of Mathematical Logic. For other uses, see Trace.
Definition
Let $P$ be a URM program.
The trace table of $P$ consists of:
- The stage of computation;
- The number of the instruction of $P$ that is about to be performed;
- A list of the contents of all the registers used by $P$ at this point.
Thus the trace table is a list of the states of the URM program at each stage.
Example
For example, consider the following URM program:
| Line | Command | ||
|---|---|---|---|
| $1$ | $J \left({2, 3, 5}\right)$ | ||
| $2$ | $S \left({1}\right)$ | ||
| $3$ | $S \left({3}\right)$ | ||
| $4$ | $J \left({1, 1, 1}\right)$ |
Let it have the following input:
- $r_1 = 7$
- $r_2 = 2$
It has the following trace table:
| Stage | Instruction | $R_1$ | $R_2$ | $R_3$ |
|---|---|---|---|---|
| $0$ | $1$ | $7$ | $2$ | $0$ |
| $1$ | $2$ | $7$ | $2$ | $0$ |
| $2$ | $3$ | $8$ | $2$ | $0$ |
| $3$ | $4$ | $8$ | $2$ | $1$ |
| $4$ | $1$ | $8$ | $2$ | $1$ |
| $5$ | $2$ | $8$ | $2$ | $1$ |
| $6$ | $3$ | $9$ | $2$ | $1$ |
| $7$ | $4$ | $9$ | $2$ | $2$ |
| $8$ | $1$ | $9$ | $2$ | $2$ |
| $9$ | $5$ | $9$ | $2$ | $2$ |