# 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 | $R_1$ | $R_2$ | $R_3$ |
---|---|---|---|---|

$0$ | $1$ | $7$ | $2$ | $0$ |

$1$ | $2$ | $7$ | $2$ | $0$ |

$2$ | $3$ | $8$ | $2$ | $0$ |

$3$ | $4$ | $8$ | $2$ | $1$ |

$4$ | $1$ | $8$ | $2$ | $1$ |

$5$ | $2$ | $8$ | $2$ | $1$ |

$6$ | $3$ | $9$ | $2$ | $1$ |

$7$ | $4$ | $9$ | $2$ | $2$ |

$8$ | $1$ | $9$ | $2$ | $2$ |

$9$ | $5$ | $9$ | $2$ | $2$ |