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Show that McCabe's cyclamate number satis?es the representational theory of measurement.
For the empirical system, consider the set of all control ?ow graphs. The relation is that one CFG is less than or equal to the second CFG if the second CFG can be built out of the ?rst by adding nodes and arcs.
The numerical system (Answer Set) can be the integers. The relation on the integers is the standard less than or equal.
The mapping is the formula e - n þ 2. There are only two operations, adding nodes and adding arcs. Adding an arc means increasing the e value. Adding a nodes means adding a node on an arc. This means that both e and n increase by 1, so the value stays the same. Thus, for any two CFGs x and y, if x is less than y, then y can be created from x by adding arcs and nodes. Thus, the value of the mapping must either increase or stay the same. Therefore, the less stringent representation condition is satis?ed. (The more stringent representation condition cannot be satis?ed, since the order on the CFGs is a partial order).
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