Hypergraphs and Degrees of Parallelism: A Completeness Result

Abstract. In order to study relative PCF-definability of boolean functions, we associate a hypergraph Hf to any boolean function f (following [3, 5]). We introduce the notion of timed hypergraph morphism and show that it is: – Sound: if there exists a timed morphism from Hf to Hg then f is PCF-definable relatively to g. – Complete for subsequential functions: if f is PCF-definable relatively to g, and g is subsequential, then there exists a timed morphism from Hf to Hg. We show that the problem of deciding the existence of a timed morphism between two given hypergraphs is NP-complete.

• Type: Conference
• Year: 2004
• Where: FOSSACS
• Authors: Antonio Bucciarelli, Benjamin Leperchey
• Keywords: Applied Computing, Boolean Function, FOSSACS 2004, Timed Hypergraph Morphism, Timed Morphism