Upper and Lower Bounds on Continuous-Time Computation

Abstract. We consider various extensions and modifications of Shannon's General Purpose Analog Computer, which is a model of computation by differential equations in continuous time. We show that several classical computation classes have natural analog counterparts, including the primitive recursive functions, the elementary functions, the levels of the Grzegorczyk hierarchy, and the arithmetical and analytical hierarchies. Key words: Continuous-time computation, differential equations, recursion theory, dynamical systems, elementary functions, Grzegorczyk hierarchy, primitive recursive functions, computable functions, arithmetical and analytical hierarchies.

• Type: Conference
• Year: 2000
• Where: UMC
• Authors: Manuel Lameiras Campagnolo, Cristopher Moore
• Keywords: Analytical Hierarchies, Applied Computing, Elementary Functions, Primitive Recursive Functions, UMC 2000