Abstract family of acceptors
An abstract family of acceptors (AFA) is an ordered pair such that:
- is an ordered 6-tuple (, , , , , ), where
- (, , , ) is an AFA schema; and
- and are infinite abstract sets
- is the family of all acceptors = (, , , , ), where
- and are finite subsets of , and respectively, ⊆ , and is in ; and
- (called the transition function) is a mapping from into the finite subsets of such that the set | ≠ ø for some and is finite.
For a given acceptor, let be the relation on defined by: For in , if there exists a and such that is in , is in and . Let denote the transitive closure of .
Let be an AFA and = (, , , , ) be in . Define to be the set . For each subset of , let .
Define to be the set . For each subset of , let .