Syntactic operators on full semiAFLs

摘要

The class of syntactic operators is defined. If a full AFL ℒ is not closed undera syntactic operator ⊗, then repeated application of ⊗ to ℒ produces an infinite hierarchy of full AFLs and the closure of ℒ under ⊗ is not full principal. If ℒ1 and ℒ2 are incomparable full AFLs, then the least full AFL containing ℒ1 and ℒ2 is not closed under any syntactic operator. If L is any generator of a full AFL ℒ closed under any syntactic operator, then all of ℒ may be expressed as finite state translations of L (without applying concatenation or star). It is shown that substitution, insertion, intercalation and homomorphic replication are all syntactic operators.