Subrecursive functions on partial sequences

The paper studies a domain theoretical notion of primitive recursion over partial sequences in the context of Scott domains. Based on a non-monotone coding of partial sequences, this notion supports a rich concept of parallelism in the sense of Plotkin. The complexity of these functions is analysed by a hierarchy of classes E n similar to the Grzegorczyk classes. The functions considered are characterised by a function algebra R generated by continuity preserving operations starting from computable initial functions. Its layers R n are related to those above by showing n 2. E n+1 = R n , thus generalising results of Schwichtenberg/M

• Type: Journal
• Year: 1999
• Where: AML
• Authors: Karl-Heinz Niggl
• Keywords: AML 1999, Domain Theoretical Notion, Partial Sequences, Primitive Recursion