June 16, 2004
Compact Set of 3d Rules
We combined the previous 3d rules into a set of seven rules that use variables. The circled pairs indicate variables that must co-exist. One variable in the pair may not exist if the other one doesn't, and vice versa. Variables that are not circled are required to exist. Variables with the same name do not have to coexist; if they both exist, however, they must be equal. The * value is still used to represent a side of a tree that has no yield, and this is the state a variable holds when we refer to it as non-existant. Some rules have the words "first" or "last" in the result. A "first" indicates that that variable recieves the value of the first (alphabetically) variable that exists of that color. Variables referred to as "last" recieve the last (alphabetically) variable of that color to exist. This compact set of rules will help us to exhaustively prove the correctness and completeness of these rules.
