Implicit complexity over an arbitrary structure: Quantifier alternations

We provide machine-independent characterizations of some complexity classes, over an arbitrary structure, in the model of computation proposed by L. Blum, M. Shub and S. Smale. We show that the levels of the polynomial hierarchy correspond to safe recursion with predicative minimization and the levels of the digital polynomial hierarchy to safe recursion with digital predicative minimization. Also, we show that polynomial alternating time corresponds to safe recursion with predicative substitutions and that digital polynomial alternating time corresponds to safe recursion with digital predicative substitutions. These authors has been supported City University of Hong Kong SRG grant 7001290. 1 

• Type: Journal
• Year: 2006
• Where: IANDC
• Authors: Olivier Bournez, Felipe Cucker, Paulin Jacobé de Naurois, Jean-Yves Marion
• Keywords: IANDC 2006, Polynomial Alternating Time, Polynomial Hierarchy, Safe Recursion