Third-Order Computation and Bounded Arithmetic

Abstract. We describe a natural generalization of ordinary computation to a third-order setting and give a function calculus with nice properties and recursion-theoretic characterizations of several large complexity classes. We then present a number of third-order theories of bounded arithmetic whose definable functions are the classes of the EXP-time hierarchy in the third-order setting.

• Type: Journal
• Year: 2007
• Where: LOGCOM
• Authors: Alan Skelley
• Keywords: Large Complexity Classes, LOGCOM 2007, Ordinary Computation, Third-order Theories